Nontechnical people tend not to deal with multiple usecases for 8P8C connectors in everyday life. Despite being fairly technical, until I googled I would have called them RJ45.
Over time, as you've noted - the vast majority of uses of 8P8C has turned out to be networking - it will be interesting to see if USB-C likewise, makes a similar evolution.
There's an RJ45S, but that's definitely nothing to do with Ethernet. Use of the term RJ45 is simply wrong, in any circumstance, as far as I can tell.
There's no term for the use of 8P8C for Ethernet purposes other than well, Ethernet, or its specific profiles ...BASE-T, as far as I can tell.
I have never once heard the phrase "8P8C" used to refer to an ethernet jack. Not once (outside of this thread) - but I have heard it used that way when referring to various 8-pin telco connections - it was a common term of art in the 90s when describing telco installations that used that configuration. When talking about Ethernet, and people are trying to be specific, they usually reference EIA-TIA-568B/A.
There are certain words, like "Bandwidth" - that, might technically mean the width of the band (typically in Hz), but have grown over time to refer to data rate as well. And that's cool - language is versatile that way.
In fact, language and terms are not set in stone.