On this NASA page on inlets it says:
In England, inlets are called intakes, which is a more accurate description of their function at low aircraft speeds.
So it depends on SE's manual of style, I'm not sure if it's been discussed before, but I think AmE is used for tags (e.g. horizontal-stabilizer with a z). In this case intake, despite being more descriptive, can be the synonym.
I don't know if I'd really say they are the same. They are used interchangeably, but "intake" generally makes me think of an engine, whereas "inlet" makes me think of a smaller opening for something else, like for the a/c packs or something. Inlet sounds odd for the engine intake. The suffix "-let" is a diminutive, usually indicating a smaller version of something else. Like "piglet" or "winglet." I've heard people use "inlet" for engines, but it doesn't sound right to me.
Interesting side note: I found out from @mins that "winglet" is basically the English equivalent of the French "aileron."