Distinct and Group By generally do the same kind of thing, for different purposes... They both create a 'working" table in memory based on the columns being Grouped on, (or selected in the Select Distinct clause) - and then populate that working table as the query reads data, adding a new "row" only when the values indicate the need to do so...
The only difference is that in the Group By there are additional "columns" in the working table for any calculated aggregate fields, like Sum(), Count(), Avg(), etc. that need to updated for each original row read. Distinct doesn't have to do this... In the special case where you Group By only to get distinct values, (And there are no aggregate columns in output), then it is probably exactly the same query plan.... It would be interesting to review the query execution plan for the two options and see what it did...
Certainly Distinct is the way to go for readability if that is what you are doing (When your purpose is to eliminate duplicate rows, and you are not calculating any aggregate columns)