How do you know when to use a paired t-test? A Poisson distribution? A regular t-test? A regression analysis?

Like for example if 7 patients are given treatment A, and 7 other patients are given treatment B, which of those tests is best to use to test the connection between treatment A and its effects? My solution manual says a regular t-test, but I have no idea why.

Also just all other probabilities and distributions. Discrete probability, binomial distribution, exponential distribution, central limit theorem, etc.?

I was told that exponential distribution is good for time intervals and waiting times. And Poisson distribution when there isn't a limit... And binomial distribution is for when the outcome is either true or false only...
Is there an easy to read guide that distinguishes all of this? My text book is really no good use at all.