They are (the terms refer to) the same thing indeed.
And yes, regarding the ambiguity, it's a no brainer: if you have money, go for the "genuine OEM" parts which are claimed to meet higher quality/special requirements (unless you really know that's bullshit: say, you make both OEM and aftermarket versions of a part
) and if you have not that much, save and comfort yourself it's just the branding, if you like
.