What is best way to make up difference between concrete and drywall in garage
I recommend you do not embark on this project.

If cost is of a concern to you, I recommend you do not embark on this project.

With that out of the way, you suggested you want this to be astetically pleasing. The best way *and functional way, to obtain the result you want is to build a wall to attach the drywall to. This means removing the existing drywall, insulating,etc - or build a wall on top of what you have.

If you do not want to do that, (which is the most expensive, and best looking approach), you could (for example), use 1 piece of 5/8, and one piece of 1/4 drywall. That gives you 7/8".

You will want to vapor barrier, or at least use greenboard due to its moisture and mold resistant design. You would then have to contact cement it and place bricks against it until dry. You will then also have to blend the edges, of the seam that now exists - and this is a NIGHTMARE.

The better approach of doing this, would be to cutback the existing drywall farther up the wall, revealing the studs, and adding horizontal pieces toed in, to use as the support behind the seam. You could still contact cement it when it meets the concrete. Or - you could use cement board, or glue in furring strips of your own instead of using double drywall sheets.

There are quite a few ways to accomplish what you want, but honestly, it isnt advisable. You can paint the concrete, or add colored aluminum as flashing. You could use molding and cut a channel in it, then use this to trim the drywall where it is already.

It all depends on the money you are willing to invest, and if you live in a wet or wintery climate, you can expect it to get damaged/dinged/dirty/wet in the first 2 years.