‘Give (something) a shot’ is an idiom which means to give something a try. The difference is that ‘give it a shot’ is used for activities that last for a short time or may be a one-time deal while ‘give it a try’ is used for activities that last for a longer period of time (i.e. Give the job a try). ‘Give it a shot’ is usually used colloquially. Here are various ways that it may be used:
John, why don’t you give the question a shot?
Speaker is asking John to answer the question.
John, it’s your turn to give the question a shot.
Speaker is also asking John to answer the question. However, it is less polite than the above command which is in the form of a question. (I mentioned before that commands in the form of questions tend to be more polite.)
Well, that’s my opinion. Now, do you want to give it a shot?
Speaker is concluding his/her response and passing the opportunity to speak to the next speaker. This is a more unique than simply asking “What do you think?”
John, give it a shot! If you need help, let me know.
Speaker is asking John to try an activity and telling him that if he needed help, he should ask.
John, give the interview a shot, I have faith in you.
Speaker is asking John to go for an interview and telling him that he/she has faith in him.