Hey TheCountador.

The best advice I can give for you is to think about what each distribution is modelling process wise and not mathematically/probabilistically/statistically.

For example binomial represents a physical model where you have n trials that are independent from each other with either a 0 or 1 outcome and then we sum up the outcomes to get X. Some say coin tosses or other things, but the idea is that you have n independent things with a success/fail for each and then look at the distribution for getting so many successes.

Now negative binomial processes model a process that waits for so many failures to occur. The geometric process is a special case waiting for one failure to occur but negative binomial allows arbitrary numbers of failures.

If you try and think in formulas only then I can see why this stuff would be confusing: the math needs to be supplemented by ideas with some kind of physical, or visual intuition and if your teacher hasn't communicated this then they aren't really a good teacher.