What terms do people use to refer to music with 3 beats per measure? I have heard the term "waltz beat" and "triple meter" but are there other (not necessarily professional) terms?
Triple and duple are the theory terms.
'Waltz time' would be just a variation of 'waltz meter.'
'Tempo di menuet' is an expression marking for something that wasn't in simple binary form, but the tempo and feel are meant to be like a minuet. I don't think this is the usage you are thinking of, but it implies a triple meter. You probably won't hear someone say "blues in Bb, tempo di menuet." :-)
Dance names like jig/gigue, tarantella, sarabande, etc. imply binary form, general tempo, and triple meters like 6/8 or 3/2. It seems reasonable to expect someone to refer to one of those dance name to indicate the associated meter. The wording probably wouldn't be "jig meter" but something more like "it uses a jig rhythm" or "with a jig feel."
'Three-quarter time' is in common use. Being three quarters of a full bar - that being recognised by some as 4/4, aka common time.
What terms do people use to refer to music with 3 beats per measure?
as I am some one of those who you’re probably mentioning with people I can tell you how some of those people could differ music compositions in a 3/4 measure from the waltz:
Minuet or Scherzo
the menuet is also a dance in 3/4 and a section in most of the suites and early sonatas and later was replaced by the scherzo in sonatas, concertos and symphonies.
I have heard the term "waltz beat" and "triple meter"
The waltz is a 3/4 where the beats are counted in a certain manner, almost syncopated. So I used as conductor of orchestras, brassbands or choirs to explain in what style they should perform the piece:
rather like a waltz!
not like a waltz, but rather as a menuet or scherzo.
but are there other (not necessarily professional) terms?
yes, there are also other terms (professional and non professional ones) most characterisizing a dance like Englisch Waltz, Mazurka or Sarabande.
As I am also one of those people I would introduce as umbrella term for all these 3/4 measures:
a threesome but why not a ternary?
Well, triple meter will be the most populary used term, but as you were asking for other terms that people use to refer to music with 3 beats ... I don't know any others than those that I and people in my surrounding are using. And if you say a threesome those who think about sex would have something to laugh about, and you will have them on your side, one of the most important things for a conductor. (maybe you will also have a few against you...)