Is there any difference between GROUP BY and DISTINCT

I learned something simple about SQL the other day:

SELECT c FROM myTbl GROUP BY C

Has the same result as:

SELECT DISTINCT C FROM myTbl

What I am curious of, is there anything different in the way an SQL engine processes the command, or are they truly the same thing?

I personally prefer the distinct syntax, but I am sure it’s more out of habit than anything else.

EDIT: This is not a question about aggregates. The use of GROUP BY with aggregate functions is understood.