Kelvin Smith Library
Musicians need various physical forms of a work, for different purposes. This is nearly unique to music as a field; let's use the example of an opera:
Full score (M1500): all the instruments, for conducting or study
Vocal score (M1503) : the vocal lines, with the orchestration arranged for piano. Used to learn a singer's part, for lessons, or for performance with piano
Miniature score (M1500): not common with opera. A full score, printed in a reduced size format, for portability
Part set (not collected for operas at Kulas): all the individual orchestral parts, for each musician to play from
Videorecording (DVD, VHS): the opera as staged performance, for pleasure or studying the entire work with its staged component
Audio recording (CD, LP): the audible content only
Steaming audio/video: video/audio in online form
Libretto (ML 47-54): the words only, in printed form
Let's see how this schema might play out with an engineering textbook, and you'll see how music is different:
Textbook
Textbook with only the facts, no explanation (doesn't exist...maybe Cliff notes?)
Small portable textbook (also doesn't exist)
(No analog to engineering; maybe each chapter published separately? Or a group exercise where each group member has their own instructions?)
Video of author teaching from his own textbook (Great Courses, perhaps?)
Audiobook of the textbook
Ebook
Textbook with only explanations but no facts?
So your first question, if the patron hasn't volunteered the information, is "are you looking for a recording or print music?"
If printed music, the next question is "Score or parts"? If they want to play an ensemble piece, they'll need parts. Note that if the piece is for a single instrument (piano, violin, guitar), there's no difference; the score IS the part. They may have other specialized needs. They may want a facsimile (unedited photoreproduction of the original manuscript or print of the piece). They may ask for an Urtext (literally, "original text") edition, generally one where scholars have compared various readings of the work and made an informed decision among them, adding nothing of their own. (In literature, this is usually called a "Critical edition", a term also used in music, but generally not as a request term.) Occasionally people will ask for a specific editor or a specific publisher (usually Henle).
If a recording is wanted, another layer of complexity is added. In essence, each different recording adds as many coauthors as there are performers (except that, thankfully, ensembles are listed as ensembles; we don't know or care who the 5th-chair violist was with the Boston Symphony in 1994). Sometimes the patron won't care who it is. If they do care, they'll ask by name. If they do, it is often easier, especially with a prolific and renowned composer, to search with the performer as author. They may also want a performance done on the instrument forms that the composer would have known (original/historical/period instruments). This maps to performer (some performers do this, some don't). A keyword of "period instruments" will catch most but not necessarily all of these (it's not a standardized term, but is included in some catalog records.) It will also matter to them what the recording medium is. Note that anything not beginning with CD is probably an LP, and you should ask the patron if that's all right. If they say yes, ask if they know how to operate a turntable. Kulas no longer offers LP records, though CIM does.
If you can't find the physical recording the patron wants, refer them to Naxos Music Library, DRAM (Database of Recorded American Music), Music Online, or Smithsonian Global Sound, all in the research databases. It would be good to familiarize yourselves with the search engines on each of these. If it's an early recording they want, they might find the analog sound recordings research guide helpful. At this level, they should definitely be consulting a research librarian.