It's likely to be railroad-specific in the 1880's. While signals appear to be common in the Eastern US, I haven't found much on Western signals at that time. It appears that block signaling began to be widespread across the US around 1898 or so.
The V&T (a western shortline about 50 miles long) never used signals - even through 1950, when it was abandoned. They just had a lot of collisions early on, then required written orders for a train to enter a section of track.
As for types of signals in that era, the Hall disc signal is one example. Another would be the ball signals, though those may have been phased out by then.