Both and it's guitar "slang"

The "true" correct term is the E3 string. (meaning E in 3rd range)

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Yep, all those are correct. I have some people who refer to them as numbers too. So, they would call the E3 a 6. This can get confusing though because some people know the strings by numbers backwards, meaning they start with 1 at the E3 instead of 6 so, it's always best to use something universal (like E3).

Heh, I've even heard some crazy ones like Fat E. :P
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Just imagine a piano and the 3rd E note.
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Im sorry, I just don't see how you could argue that hardcore isn't metal. That just seems arrogant to me.

Yes, its its own kind of metal, but its still metal.
I just call it low E, or.. E, on computer etc i refer to high e as 'e'.
Call it the sixth string, or the low E note if it is tuned to E.
Otherwise it is the low whatever note the string is tuned to.