Hinder and inhibit are very similar words in terms of their meaning, however there is a slight difference. Inhibit means that to stop an action or forbid an action from taking place. For example, one could "Medication was prescribed to the patient to inhibit the growth of any bacteria". As you can see here, the word inhibit suggests that the medication stops an action - which in this case is the growth of bacteria.
Hinder means to cause a delay, to interrupt, to make difficult to accomplish. Thus this word suggests that the action being hindered was in fact completed at some point but that it was very challenging to do. For example, one could say "If you do not get enough sleep, you will hinder the progress you've made in school". Using the word "hinder" here suggests that you will continue to make progress in school even if you have not had enough sleep BUT the lack of sleep may result delay your progress.
However, the differences between these two words are small so if you make a mistake, it really isn't at all a big deal. And, as a native English speaker, I can say for certain that the vast majority of people do not use these two words in casual conversations.