I have a battery maintainer hooked up to my ‘18 R. Previously, I failed to switch the maintainer to “AGM” and it maintained the voltage at 13.7 volts. Realizing my mistake, I switched it to the “AGM” mode and since it maintains the battery at 13.4 volts. Why the difference?

 

Both those readings seem a bit high to me, I use my battery maintainer all the time and it always shows 12.6 - 12.8 volts.

 

One possible reason for the difference could be that you have left the car for a long time on the maintainer.
On my Ctek the instructions explain that for a while, the battery is maintained at 100% charge. After a while, with mine I think 2 weeks, it changes to maintaining the battery at about 95%
Not sure if that's the answer, but it's a possible reason for a fall in voltage.
I agree though that both seem a little high. 13.7 volts is the normal state for a battery when the engine is running. Could it be your meter isn't reading correctly?