I apologise for mixing terms. Jail and Prison? Do you disagree this is a point of difference? Americans also don't seem to talk about being on remand. In police custody is unwieldy, I agree.
Although that distinction is rarely relevant in casual conversation in practice. People say "jail" and mean "prison" all the time.
It can definitely come across as a “Frankenstein’s monster” type of pedantic correction, but they truly do mean two different ideas in the US