No, they are not the same thing.

The Military Service Act was the act that introduced involuntary conscription of Canadians into military service during the First World War. It was passed by Borden in August of 1917 because voluntary recruitment was lagging, and Canada needed replacement soldiers after the Battle of the Somme.

There was a lot of political and public opposition to conscription - particularly in Quebec - and the passing of the Military Service Act, while seen as necessary, drove many supporters away from Borden's coalition. It was very likely, without some intervention, that Borden would lose the next federal election.

Borden had already postponed the federal election that should have happened in 1916 (pointing to the First World War as an emergency requiring the full attention of the government) but he could not postpone it past 1917. Knowing that the Military Service Act would be at risk if his party lost the election (to Laurier's Liberals) Borden passed the Military Voters Act which allowed the soldiers overseas - regardless of their previous eligibility - to vote in the election.

This helped Borden's Unionist party win the election in two ways. First, most soldiers favored conscription as the conscripted solders were to relieve them on the front. Second, the Act allowed the party they voted for to place any votes not clearly marked for a particular riding to be put into any riding selected by the party. So the party could "top up" into a win any ridings that were a close race with votes from soldiers overseas.

So Borden won the election and conscription remained in place.