Aftershave can be a balm, but can also be a lotion (commonly thought of as a splash containing either alcohol or not). Balms are typically thicker and heavier than a lotion (splash).
The varieties are nearly endless. Balms, lotions, creams, milks, splashes..... clear fluid or opaque, white creamy in nature. An after shave is anything that you put on your shaven face to soothe, disinfect, heal, or condition.