Nope. Case in point, Solar Macharius was a Warmaster, but not the Lord Commander Militant. A Warmaster, in the modern sense of the word, is the military commander of a Crusade, and of such high rank and station that he is second only to the Lord Commander Militant himself.
A good way to think of it is this*:
- The Lord Commander Militant is for the Imperium in its entirety
- The Warmaster is for a Crusade (and thus a fixed task and time period), which might draw upon the resources of many a sector
- The Lord General Militant is for a specific Sector
* At least I think it is; perhaps Baron or another master of the fluff might correct me if it's not?