The 2 videos here are an overview of the different kind of stamps and positioners available today and why I chose the one I use. These are a bit long so I have linked them to the youtube channel. Enjoy
Stamp Positioners Part 1
Stamp Positioners Part 2
Stamping Started for me with the red vulcanized rubber stamps mounted on wood blocks. The blocks would have an indexing on the back to show what the art was and would usually would have an indent in the wood where your fingers would go. The rubber was backed with a foam cushion, allow for some give when you pressed the stamp. In the early days we would stamp the art with the stamp on the block before we would actually stamp the image on the block so we could know what the same on the other side looked like. The blocks and stamps would be in all shapes and sizes. There were also companies that sold the rubber stamps on sheets where you could either mount them on a block yourself or us some kind of cushion underneath the paper to give some give. 
This is my wall in my studio with many of my wood mounted stamps. I just can’t let them go I love them too much.
Later came the cling mounted stamps. They took up a bit less space as they did not have the wood blocks. You would mount the cling mounted stamp to an acrylic block (Mount) and you reused them over and over. A person usually just had a set of different sized blocks to accommodate different sized stamps. In the beginning these did not stick very well and would fall off when you would turn the block over. I often coated mine with a repositionable glue to keep them from doing this. The cling stamps today have come along they don’t seem to have this problem as much. Red Rubber (the rubber can come in different colors) still gives the best ink transfer especially for fine detail images. 
Then came the clear stamps. There are two kinds. Acrylic/silicone and photopolymer. The concept is the same as unmounted cling rubber stamps the the image is out of a clear substance. the Acrylic/silicone are the lesser expensive, they are much stretchier. They tear easier and do not hold the ink near as well. You will often find them giving a blotchy transfer of ink. I have a few but not many. These will also degrade and yellow over time.
Clear photopolymer stamps are a bit firmer and hold the ink a bit better. They will often come with a film on them from the manufacturing process but you can clean that by just rubbing the stamp with your finger or a dry cloth, especially with more solid stamp images. You can also stamp your image once with versamark (watermark) ink that will help. 
Anyway moving along, as this is not about the stamps themselves but how to position them on your projects. In the early days there was the Stamp-a-ma-jig. It was a plastic brace with an elbow and a plastic sheet, the sheet would fit into the elbow. You would then line the wood or clear block in the elbow, after inking up the stamp, and stamp the image onto the plastic. This is an index sheet allowing you to decide where you want the image on your project. Once you place the plastic down, put the positioning tool against the plastic, move the plastic away and put the stamp into the elbow as you did when stamping the image onto the plastic. Leaving the positioner in place, check the image to make sure you have a clean stamping if not you have the positioner in the correct spot to go through the stamping process again. If you moved the positioner you can line up the plastic again with the stamped image. Sound complicated? Well, it was in a way. While it worked you would often just not use it and end up with a ruined project because you did not get a good image stamped down. There is still a version of this sold today, not exactly the same but the theory is the same. I will link it in this post.
Along came the MISTI, Most Incredible Stamping Tool Invented. My stamping life was changed! This tool has a magnetic pan (about 9.5 by 8.0), it comes with a pad (for use with clear stamps) and a bar magnet (early on it came with 2 round magnets), to hold your project in place. You place your paper inside the tray, place the stamp where you want it on the paper, close the door to pick up the stamp, ink up the stamp on the door and close the door again. As long as your paper was in one of the corners of the pan the stamp would be in the exact same place each and every time. This allowed for stamping and re-stamping to your hearts content. Can I say I was happy? Why yes I loved this thing. But I am always looking for bigger and better. 
As technology changed along came the stamp positioner from Tonic, branded by Tim Holtz. 
Now, this tool is not easily available in the US because of an agreement made between Tonic and My Sweet Petunia (maker of the MISTI) because of an alleged Patent Infringement (f you wish to read the court documents go here https://insight.rpxcorp.com/litigation_documents/13192436). This tool works similarly to the MISTI however to switch between clear and rubber stamps you would remove the door, turn it over and re-insert it into the hinge. The platform does not have a grid in it and the makers like to say you could stamp a larger piece of paper because of the open design of the right and bottom sides. However, there is a ledge at the side preventing you from mounting a stamp anywhere near the bottom or right sides of the platform as this ledge would impede the stamp from sticking to the door. The other problem with this tool was if you used the upper left corner to position the stamp and tried to transfer an image from there the plastic door was too stiff close to the hinge/corner. To get a decent placement you would need to stay in the center of the door, but without a grid to mark the position of the paper it was difficult at best to re-position the paper in the exact same spot. The sponsors of this tool started using a product called sticky grid to stick the paper to the platform which works but its something else to buy. I will have this linked below along with the sticky grid in case you are interested.
Next came the Stamparatus from Stampin UP. And what made this tool intriguing to me was they placed a hinge and a door on the left and the upper part of the tool. This allowed for multi-step stamps to be set up all at once and to be stamped down by inking and stamping one door then inking and stamping the other door. The problem with this tool was the same as the Tonic one. You cannot stamp in the upper left corner close to the hinges as the stamp is not able to touch the platform from this location which makes stamping just as frustrating as not having this tool at all. I was very disappointed because they allowed you to buy extra doors separately and they originally carried a cute bag to carry it all together which I loved! I always wondered why this company had not been sued as well because the concept was so similar to the Tonic platform. Well today as I was researching for this blog post I found that My Sweet Petunia had sued StampinUp! (If you would like to read the court papers go here https://casetext.com/case/my-sweet-petunia-inc-v-stampin-up-inc). I own one of these it gets packed in its cute little bag and never gets used. I always go back to my MISTI.
There are other stamp positioners out there that work on different concepts. I will also link them below if you are interested. I also saw a new one being demonstrated at Creativeation 2022 by Altenew. I have not seen that one come out on the market yet. None of these types have a hinge/door system.
The MISTI has 3 sizes, mini regular and the memory (12×12). There are some alignment accessories sold as well that allow for some different techniques you can do with this tool.
Whatever positioning tool you decide to use I will tell you they change how stamping is done, and a stampers confidence in getting a clean clear imprint of the image on the stamp. It will change your stamping life, like it has mine!
Here are a few shopping links for the products mentioned here:
Tonic Stamp Positioner https://amzn.to/3yPF0DL
MISTI Stamp Positioner https://amzn.to/3z4XQal
Sticky Grid Sheets https://amzn.to/3bY9ieB
Wendy Vecchi Stamp Positioner https://amzn.to/3bYfgw2
Clear Acrylic Stamp Blocks https://shop.catherinepooler.com/collections/blocks/products/acrylic-grid-10-block-bundle
Stamp Platform We R Memory Keepers https://amzn.to/3c5fgKw