It was the //e and //c that had built-in lowercase support.
I mostly remember that the RAM upgrade changed the gauges in MS Flight Simulator from octagons into rounder circles.
I actually didn't realize until I had to use a ][+ at school later that some computers didn't do lower case :)
Lowercase and 80 columns were available from third-party vendors for both the II and the II+.
Source: I still own my II. Also:
https://archive.org/details/Videx_Videoterm_Installation_and...
It was common for Apple resellers at the time to sell them with third-party add-ons.
BASIC and the monitor were stored on ROM chips on the motherboard. The II and II+ were basically the same computer with a different set of BASIC ROM chips installed.
Edit: It is actually possible to have both sets of ROM chips installed if you use a Firmware card. Very handy!