Think of it as two different variables. You have your focus target and your player target. Each can be set to a different target. So, you can have two things targeted at once. These commands are for that purpose.

/assist will set your "player target variable" to whoever you are assisting. You can use things like /assist party1, /assist Joeblow. This variable resets with a click of the mouse or the mob dies or you reissue the command. Although /target is more appropriate in this context than /assist, but both set the same variable.
/focus will set your "focus target variable" to whatever target you want depending on the command that follows it . This variable will remain set until you reset it by reissuing the command or a reset command.

There are other more complex arguments as well ,as others have pointed out above.

You may be referring to assisting and following your main in a Boxing group. In this case, the whole benefit of a "focus targetless leaderless" (or FTL) macro setup is so that if your main dies you will still be able to function because you just end up getting your target information from a different toon. This takes advantage of the /focus target variable. With just a simple /assist based macro, if the person you are assisting dies, well, you no longer can set your player target without using other means. At least, that is what I understood it to be. Never used it. I think it has more use in a PVP environment. Of course, there are more than one way to do this and you don't necessarily need to use /focus at all, but would likely require more macros etc..