Is it treated exactly the same each time and/or at each attraction?
No. Even on the same attraction, the GAC is not always handled the same each time.
Exactly what happens depends on how busy it is, how many other people with special needs are there at the time and staffing.
Some times you may be sent thru the regular standby line, ocassionally another access; Occasionally the person with the GAC and a member of their party will be given an alternate place to wait while the rest of the party goes thru the standby line - and then meet up with them when they get to the front. Sometimes you might be given a slip and told you can come back at the time written on the slip (usually equal to the standby time); very ocassionally, you might be taken right in. It depends on what they call "attraction considerations" (which is basically the things I listed in the second sentence).
What happens will also depend on the stamps on your GAC. For example, if the GAC is for a place to out of the sun, you will be routed to the regular line if the sun is not a problem when you arrive at the attraction.
If you come back later, you may be handled differently. Even on the same attraction on the same day. People sometimes think that means one of the CMs did something 'wrong'. What it usually means is that conditions were not the same both times.