Spanish makes a subtle distinction between proverbio [proverb] and refrán [?]. This distinction was described well here. I'll attempt to translate informally from that answer.
Although the two words can be considered synonymous, the connotations are different:
refrán: a colloquial, folksy saying or piece of advice. It needn't be about something weighty. It often features a rhyme, making it catchy and easy to remember.
proverbio: a bit more serioius than refrán. Generally speaking, it doesn't provide advice about banal matters, but has more of a moral, ethics tone.
Marzo ventoso y abril lluvioso sacan a mayo florido y hermoso. [Loosely: April showers bring May flowers; literally: Windy March and rainy April bring out a flowering and beautiful May.]
The subject matter of this refrán is the weather.
A proverb, on the other hand, is more formal, has a more serious subject matter and attempts to teach something.
Here's an example of a proverb:
No es oro todo lo que reluce. | All that glitters is not gold.
My German spouse informs me that refrán seems to be similar to Bauernregel (guidance for farmers), but with a particular focus on the weather. For example
Der April macht was er will. | April does whatever it wants to.
My question is what is the closest equivalent to refrán in English?
Edit after question was closed as a duplicate of a question that was closed because a sample sentence wasn't provided:
Spanish has a charming refrán that's relevant to your situation: [....]
An additional thought: I'd like ideally to find something as graceful as, for example, "turn of speech." But that won't work because a turn of speech is a fragment, not necessarily a whole sentence.