What is the difference between 受 and 收?
Considering 受 and 收 as the translation of the English verb "to receive" is confusing, as it really depends on how they are used (a lot of expressions use those two words). I think the difference is easier to see with examples.

受 seems to be used for immaterial things (such as feelings, influence, etc.) Its passive connotation really depends on the context or other words in the sentence/expression.

ex: 


他很受欢迎。 - He is very popular.
他受到你的影响。- He is influenced by you. (which can be good or bad).


Even when the character 受 is used in words, it is for abstract things:
感受 (a feeling)

收 seems to be used for material things (a letter, a document, a SMS).
ex:


我收到你的短信。 - I received your SMS.
别忘记收垃圾。- Don't forget to collect the trash.


Same things here, when 收 is used in words, it describes material things:
收音机 - Radio (set). Literally the device receiving sounds.

I hope this answer your question.
I wish you pleasure and success in your studies!