Hey Parker! Both actions you mentioned are Browning recreations of the classic Winchester 1885 "high-wall" actions, designed by none other than John M. Browning.
They are both completely different on the inside from the originals, and the trigger is significantly different between the M78 and the M1885.
The M78 was introduced in the late '70s, and dropped from production sometime in the '80s. The M1885 was updated, redesigned somewhat (especially the trigger) , and reintroduced in the '90s in several models...M1885 Highwall, M1885 Lowall, Traditional Hunter (both high and low wall versions), and BPCR competition models. They are out of production again, to my knowledge, though you can still find new ones for sale here and there.
There are a lot of differences between the different models (stock shape, barrel length, barrel shape, sights, etc.), but the basic rifle, whether M78 or M1885 is still a great rifle, so pick the one that you like best and have fun!
Greg