What is the biblical basis for distinguishing between spiritual gifts and church offices?

I've heard Christians claim that someone may have the "gift of apostleship", even though they may lack the "church office" of apostle itself. Same for prophet, evangelist, teacher, etc. What is the biblical basis for making this distinction? What biblical reasons are there for talking about the "gift of X" and the "church office of X" as two separate categories, where X can be apostle, prophet, pastor, evangelist, teacher, etc.?