"Snap a picture" is more casual. To me, it implies something that was not planned, or that you do quickly.
Ex) Can you snap a picture of that?
Ex) He quickly snapped a picture while we drove by the monument.
If you are referring to a photographer or anybody who put time into framing and lighting the shot, then "take a picture" would be more suited.
Ex) Could you take a picture of us in front of our new car?
Ex) He took pictures during the ceremony.
