Compressed Yeast: Often called cake yeast. It only lasts about 2 weeks and must be refrigerated. I actually haven't seen it in the US, but I used it in Europe. It is basically a soft block of yeast that needs to be placed in water to break it up. It is equal to 1T of regular yeast.
Active Dry Yeast: When a recipe calls for yeast, this is mostly likely what they are talking about. It is sometimes abbreviated ADY. This yeast need to be rehydrated in liquid at temperatures between 105 and 115` F (If your pinky is comfy, your yeast probably is too!). If you use hotter liquid, you risk killing the yeast, cooler and the yeast membrane gets too porous and can allow the cell contents to leak out and become ineffective. If your dough is sticky and inelastic, that is a probable cause. Active dry yeast has the largest cell size of the yeasts. To see if your yeast is still good and active, rehydrate in a 1c water with 1/4t sugar per tablespoon of yeast. If you see yeast bubbles coming to the surface after 5-10 minutes, you have healthy active yeast and you can proceed with your recipe. If you don't you need to buy fresh yeast, or adjust the temperature of the water.
Rapid Rise Yeast and Instant dry yeasts (IDY) were developed to overcome several of the problems with Active Dry yeast. They can both be added directly to recipes without rehydrating first. They tolerate higher temperatures of water and are harder to kill. They both have shorter fermentation periods. This means you don't have to let your dough rise for as long to achieve the same results. Instant dry yeast works even faster than rapid Rise yeast. The cells of instant dry yeast are skinnier and longer. Instant dry yeast can cut the rising time even further.
To substitute Instant Dry yeast or Rapid Rise yeast for a recipe calling for regular yeast, you can skip the step of rehydrating in the water, to keep things simple I add things in the order called for in the recipe, but I don't let the yeast and water sit together for 5-10 minutes. I add all of the liquid, the yeast, sugar, flour and start mixing, adding the remaining ingredients and then slowly adding the rest of the flour. Just watch the rising times as they may be faster than what you are used to, or called for in the recipe.
To substitutre active dry yeast in a recipe calling for SAF yeast, Instant dry yeast, or rapid rise yeast make sure to mix the liquids, some of the sugar and the yeast together first. Allow it to sit until it starts to bubble and you can tell the yeast is alive and working. Then continue with the recipe. Adjust your rising time by adding extra time, I usually find it takes up to twice as long to achieve the same amount of rise with active dry yeast.
I definitely prefer Instant dry yeast (SAF is a common brand of IDY) for my whole grain bread making. My bread rises at least 10% better with IDY yeast versus rapid rise yeast and a good 25% higher than with active dry yeast. I use regular yeast and rapid rise yeast in my pita breads,flat breads and rolls that I am not in a hurry with.
Instant Dry Yeast (I buy it at Sam's Club, it comes with 2 1pound packages, they feel like bricks) Make sure it says IDY or SAF yeast
Rapid Rise yeast You can find it like this at almost any grocery store, it also comes in little jars. Sometimes called Bread Machine Yeast
Active Dry Yeast. Available at most grocery stores. Also available in 4 oz jars.
I took some close ups to try and demonstrate the differences in the types of yeast. My IDY yeast has some rapid rise and active dry yeast mixed in, that is why there are different sizes.
If you look closely, the rapid rise and active dry yeast are both slightly lighter in color than the IDY. The active dry yeast has the largest cells, then the rapid rise, and Instant dry yeast has the smallest. The IDY yeast cells are narrower, but slightly longer than the Rapid rise yeast.
Top: Rapid Rise Yeast, Instant Dry Yeast
Bottom: Active Dry Yeast