According to the OED, employee does indeed mean "a person employed for wages."
Associate could have several meanings and origins; personally, I suspect the original motivation was to find an alternative to employee which sounded more impressive and designed to make the employee feel more important.
However, more technically, associate could have several relevant original meanings:
OED 1.A.1 Joined in companionship, function, or dignity.
3.A.3 United in the same group or category, allied; concomitant.
B.B n. [the adj. used absolutely.]
1.B.1 One who is united to another by community of interest, and shares with him in enterprise, business, or action; a partner,
3.B.3 One who shares an office or position of authority with another; a colleague, coadjutor. spec. An officer of the Superior Courts of
Common Law in England, ‘whose duties are to superintend the entering
of causes, to attend sittings at nisi prius, and there receive and
enter verdicts,’ etc. (Warton.)
4.B.4 One who is frequently in company with another, on terms of social equality and intimacy; an intimate acquaintance, companion,
5.B.5 One who belongs to an association or institution in a subordinate degree of membership, without the honours and privileges
of a full member or ‘Fellow.’
The origin of the now-common associate could be descended etymologically from a combination of people in frequent company, sharing common interest, and belonging to an institution in a subordinated capacity.