What exactly is the difference in name between the Bass "E" and the Treble "E" strings? Is there a specific term for them?

High E (Treble) sometimes indicated as lowercase "e".
Low E (Bass).

I *think* the low E can also be referred to as "first E" and the treble e as "second e", but not entirely sure. If there are other names, I don't know them.

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Whoops, the Dark Side took me again...

There is also a more technical designation in which -

The bottom string open = E2

The note on the 4th string 2nd fret = E3

The top string open = E4

The top string 12th fret = E5

Some electronic tuners will show these different names for E notes

btw - The bottom string on bass guitar = E1

Thank you both for your replies. Very helpful! That's exactly what I wanted to know!