The meaning you listed seems to correlate across many Romance languages and caused me to start looking deeper. I found an Anglo-Norman dictionary [0], which lists meanings very much in line with those listed at Etymonline [1]. I can't explain the difference... The listed Latin root seems to allow the noted Anglo-Norman and later English meaning [2]. But modern Romance languages seem to have standardized a meaning similar to what you mention.

There does seem to be widely-attested noun forms like French sorte, Italian sorta with a meaning along the lines of "type" or "kind".

[0] http://www.anglo-norman.net/gate/

[1] http://www.anglo-norman.net/D/sortir

[2] https://en.wiktionary.org/wiki/sortior#Latin