What is the term to describe when people words have veiled or alternate meanings?

Sometimes people , especially people practicing covert aggression, tend to talk in highly ambiguous terms when interacting with someone , which leaves the other person wondering - were they really saying these things about me, or to me indirectly while seeming to talk about that other person or other thing or telling me this story, and it leaves the person under the verbal aggression in a confused state as to whether they were imagining the messages or the abuser really was talking about them. Somewhat like dog whistle, but done on a one on one basis. Is there a term in English for this?

Solution 1:

One current term for this kind of agressive speech is coded language. The term refers to the speaker's intent to conceal an often derogatory meaning while sharing that meaning with those who might share the speaker's prejudices.

Examples harvested from the free-range internet include

Vox (Feb. 2016) The sneaky language today's politicians use to get away with racism and sexism

Buzzfeed (Feb. 2015) 14 Words That Carry A Coded Meaning For Black People

Solution 2:

The website WordHippo is very helpful when you are searching for synonyms and antonyms.

I took the word enigmatic (which, by the way, is a good word for the phenomenon you describe) to WordHippo, and here is what I found:

ambiguous cryptic mysterious obscure unknowable dark Delphian doubtful enigmatical equivocal incomprehensible indecipherable inexplicable inscrutable occult oracular perplexing puzzling recondite secret sphinxlike stickling stumping teasing uncertain unfathomable unintelligible

I'm sure you can find at least one or more words which describe the seemingly covert aggression you describe.