TF-4 is an alkaline fixer, Ilford rapid fix is an acid fixer.

TF-4, and the other alkaline fixers (tf-3 and archifix to name a couple), are used because

a) They wash out more easily from the film and paper emulsions (good for achival properties) and
b) Because they have less effect on the stain created by staining/tanning developers - Pyro, Pyrocat HD, Dixactol etc.

Not neccesarily in that order

When using an alkaline fixer it is normal/recomended to use just plain water as a stop bath. This keeps the emulsion from acidity stopping stain loss and the possibility of pinholes in film developed with a carbonate accelerator (as some developers have). A plain water stop is just as effective as an acid stop just slightly slower. Hence the post above that points out that, for short developing times, the development has to be stopped rapidly. In that case then, you might use an acid stop. For any other times it is not at all neccesary.

What are we doing when we stop a film? If using plain water then we are diluting the developer so much that it stops working. So I use two 30 second stops of plain water (at developer temp) with constant agitation. If using an acid stop, we are stopping the developer from working because it will not in an acid environment. You can see then that the water stop is slightly slower at stopping the film. At development times of over 5 minutes, this speed of stopping is not important. Just make sure you do it the same everytime..... be consistent.