Based upon the photos here are some thoughts and questions;
1) It looks like the result you're after has,no, if any, stain in it. It looks to be a clear coat over natural wood.
2) The 1st 2 pictures show that color has been used on the chairs. While you have sanded a lot of color off the chair, some of the color you see is from a dye stain. Dye stains penetrate the wood and are very, very difficult to completely sand off. In order to remove the color to get the finished result you're after, you'll have to bleach the color out.
3) You can start with ordinary household laundry bleach, and apply liberally to all surfaces. Let sit for 24 hours and then evaluate. You may have to apply a 2nd coat & while still wet, LIGHT sand with a 400 grit Wet/Dry sandpaper (available at Home depot or a good hardware store). Then wait 24 hours and evaluate. Most of the color should be gone. Where some color remains, light sand those areas with the 400 grit paper, always going in direction of the grain.
4) The info you received on the net is all about sealing wood before applying stain, so as to prevent blotching and ensure finish adherence. If you've removed all the color, use next step. If color not all gone let us know.
5) Light sand with 400 grit and vacuum up all dust. At this point you can get a look at what the wood will look like if you just apply a coat of clear finish. To do this, take a damp (not wet, damp) rag and rub on a couple small areas. This will show you what it will look like with clear finish. If you like the color go to next step. If you don't like color decide what color you want - brownish, reddish, orangeish, etc.
6) Buy a product called Sealcoat. It's diluted shellac. Apply to all surfaces. Once you brush onto an area do NOT go back over that area. Let dry for 2 hours. Light sand with 400 grit and vacuum up all dust. Apply a couple coats of the finish you like following instructions on the can
Bob "Boardman" Borders