"Deshi" is commonly used in traditional contexts, and implies one has attached oneself to one particular teacher for instruction. It's not commonly used in modern budo, where people tend to belong to organizations rather than learn at the feet of one particular teacher. It's still used in koryu, by which I mean not just bujutsu but also tea, ikebana, and similar traditional schools where there's a transmission in a lineage. Also in sumo.
Thanks, Joshua, that clarifies quite a bit and fits well with how I've heard it used in sword crafts (polishers, kinko, smiths, sayashi, etc.) often where there are also issues of lineage (in one sense or another). It usually seemed to be about personal transmission from one to another and not just "I study this or that" in a general sense. Makes sense. Thanks again.