I would suggest a practical definition of a “spin” is where classic stall recovery control inputs will not recover the airplane and indeed will exacerbate the situation.
I don't think such a definition can cut the mustard. The characteristics of some aeroplanes could put a lie to that one. Think of the Tomahawk losses during its early days.
However I have never seen an airplane that will not recover with a conventional stall recovery technique if the stall recovery inputs are correctly and forcefully applied before the airplane has completed more than 180 degrees of yaw after departing controlled flight.
Following a discussion with a number of competition pilots: it was common to use pitch alone to recover from a spin during the first two to three rotations (still incipient). Keen to try this I used the club Robin 2160. This technique worked perfectly, recovering precisely onto per-determined headings, as promised. I then tried the same holding in the spin for 6 rotations (a fully developed spin is said to take place after 4-6). On recovery it was impossible to shift the stick; fully aft it was as if set in concrete. Only after a conventional recovery using max opposite rudder was it possible to shift the stick but only when the rotation slowed. Recovery was then conventional.