We use both of them in the sense of "little ". But the second one "немножко" softer, if I may say so, we use it to say even less then a few, that is quite a bit or slightly. For example : Ты можешь взять немного ягод из корзины. Попробуй пожалуйста моего пирога, ну хоть немножко. Also we've got the word "немножечко", and we use it the same way as "немножко".

Synonyms

there is no difference. you may use both of them in the same situations.it's not important to pay any attention)

"немножко" is slightly less than "немного"

bit and bitty