I see some 18W lamps say SOX, some 18W lamps say SOX-E. Not that it really matters, because there is only one lamp of those dimensions and it's corresponding ballast, but I would like to know. To be clear I am not referring to the rarer 18W SOXD-E, just the run-of-the-mill 18W LPS lamp.

I know that SOX-E lamps have generally thinner discharge tubes and thicker ITO coating, but obviously that would have to be the case anyway for a lamp this small to be practical. Does anyone know it's official name?

Edit: also same question for the far rarer 10W SOX lamp

Some companies, like Osram, called it SOX, others, like Philips, called it SOX-E.
The 18W lamp predates the invention of SOX-E, but it is basically the first time SOX-E style technology is put into a commercial production lamp. I suppose when SOX-E was released a few years later, it made sense to put the 18W in the SOX-E class.
https://www.lamptech.co.uk/Spec%20Sheets/D%20SLP%20Philips%20SOX18.htm
https://www.lamptech.co.uk/Spec%20Sheets/D%20SLP%20Philips%20SOXE26.htm
Personally, I call it 18W SOX, not SOX-E. And when I list SOX power ratings, I say 18, 35, 55, 90, 135, and 180. I don't include it when I recite the SOX-E powers of 26, 36, 66, 91, and 131.

Very interesting, thanks! I did not know it was made before SOX-E. And as most SOX-E lamps are meant to replace SOX lamps, but the 18W one isn't, I will just stick to calling it SOX.