Why 2 words for the September to November months, but only 1for the other season

I’m talking about “fall” and “autumn”.

AFAIK, there are no other words that mean “summer”, “winter”, or “spring”.

Why/How did we get two words for fall/autumn?

From this site, I found the following:

Not much, but it’s something…

Lent is another word for Spring, albeit archaic in that sense.

The original meaning of summer seems to have been ‘year’. Before the knowledge of calendars, prehistoric Indo-European people counted their age by summers. At least, the proto-Indo-European word *samos that became summer in English, also became the Sanskrit word sama meaning ‘year’. It might be related to the IE root *sem- meaning ‘one’ (as a unit of counting years?).

Modern Brits think of “fall” (in the sense of ‘autumn’) as an Americanism, but in fact their ancestors used “fall” in that sense back in Elizabethan times. In many respects, the American use of the language is more conservative than the British.

Also archaic, but does give us the “vernal” equinox: