- Άλογο is used in practically all cases.
- Ίππος is only used by scholars and in very specific cases. Eg: Δούρειος Ίππος (= Trojan horse). It also means horsepower.
- However, ἵππος is the ancient Greek word for horse. Therefore, it is the root of some modern Greek words related to horses. Eg:
- ιππεύω = ride (a horse)
- (η) ιππασία = horse riding
- (ο) ιππότης = knight
- (ο) ιππόδρομος = hippodrome
- (ο) ιπποπόταμος = hippo [in ancient Greek: (ὁ) ἵππος ὁ ποτάμιος]
I hope this helps. :-)
Apparently the etymology of άλογο is exactly what it sounds like: "wordless" (https://en.m.wiktionary.org/wiki/%CE%AC%CE%BB%CE%BF%CE%B3%CE%BF), because horses don't speak.
(More precisely, to distinguish military animals from soldiers.)