Is there a term describing a saying or idiom where you can swap one word and it means the same thing?

I think I've seen this before.. often there are sayings where people substitute one word for another one that sounds similar, however, this doesn't end up changing the overall meaning of the idiom.

Something like "coming down the pike" vs "coming down the pipe".. one is correct but they really mean almost the same thing. "Peaked my interest" vs "Piqued my interest", "deep-seeded" vs "deep-seated"

These could be considered:

eggcorn

a malapropism or misspelling arising from similarity between the sound of the misspelled or misused word and the correct one in the accent of the person making the mistake

malpropism

the unintentional misuse of a word by confusion with one of similar sound, esp when creating a ridiculous effect, as in I am not under the affluence of alcohol

solecism

the nonstandard use of a grammatical construction

pike vs pipe source

down the pike is entered in the dictionary with two meanings: "in the course of events" and "in the future."

The unfamiliar use of pike might partly explain why we sometimes see the phrase rendered as down the pipe, particularly in the sense referring to anticipated future events:

The phrase also suggests a conflation with a similar one, in the pipeline, used for projects or anything in a state of development, preparation, or production. Pipes and pipelines, with their ability to carry a continuous flow, suggest a streaming resource, which is why we speak of music being "piped" into a store, or a baseball team's "pipeline" of prospects coming up from the minor leagues.

This one seems to be less of a mistake, and more of a changing of phrase

coming down the pike is the original phrase

peaked vs piqued vs peeked source

Peak is the verb you use to talk about reaching a maximum, or coming to a highest point, literally or figuratively

Pique is the oddball of this trio. ... It comes from a French word meaning literally "to prick," ... Now, however, it's most often our interest or curiosity that gets piqued—that is to say, our interest or curiosity is aroused:

piqued my interest is the correct phrase

seeded vs seated source

Deep-seated is the adjective you are looking for to refer to something that is firmly established

seed has another meaning that encourages some confusion with seat: "to rank (a contestant) relative to others in a tournament on the basis of previous record." English speakers clearly experience some cognitive dissonance regarding this sense of "seed": the verb seed means to plant something so it can grow

The examples relating to seed don't seem to ever be prefixed with deep

deep seated is the correct phrase