I defer to M.Ted, who actually sounds like he knows what he's talking about. As he mentions, guitar chords often delete notes--the common C7 has no G in it. There are also quite a few chords I've seen lacking the root note (1). The 9th and 13th chords usually have to sacrifice something (having 5 & 6 different notes, respectively), but they need to keep the flatted 7th and the 9th &/or 13th to retain their character, so 1, 3, or 5 usually go. If I understand M.Ted correctly, these are not technically properly called chords, but in practical applications that distinction is usually not made. I guess it depends on how picky you need to be in a given situation. In a 9th chord that was missing a 1 or 5, it would normally just be written D9. If someone asks, or one is writing a textbook (or a post like this-BG), then the missing note would be pointed out. (The 3rd is almost always retained, as it's key in distinguishing major from minor.)

I've recently been introduced to swing chords that are played on the 3rd, 4th, and 6th strings (the other strings are muted). All of them are minus at least one note, and it's sometimes the 3rd--one form, for example, is used as either a (dominant) 7th or a minor 7th. And I understand that some rock & roll rhythm players typically use 2-note "chords". It really boils down to what sounds good in the context of the particular tune. Consistency? We don't need no stinking consistency! (BG)