Board games are typically classed as "competitive" or "cooperative",
but I think there's more gradation possible.
At one end of the scale is something like Chess or a
traditional wargame: you are out to defeat your opponent, and anything
you do inside the rules is considered legitimate. I think this leaves
one open to the sort of boundary-pushing that I've always seen as bad
behaviour: the rules say I can do this, so I'll go right up to the
edge of that the rules allow in an effort to throw my opponent off
their game. (See, for example, the history of shenanigans in
high-level chess tournaments, quite separately from what is explicitly
regarded as cheating.)
Slightly less extreme, perhaps I can't attack you but I can make your
life harder: I take that card or worker placement spot that I know you
wanted. This is less far into the "take that!" space but can still
feel mean.
I see racing games as somewhere near here: it's still competitive, but
the rules generally disallow direct attacks on the other players.
(E.g. they may allow me to collide with you deliberately, but that'll
damage me as much as it does you.) Something like the unexpectedly
good Rush 'n' Crush does allow attacks, but the opportunities for
performing them are rare enough that they aren't a major part of
gameplay.
There's also the "cooperative with traitor" style like Shadows over
Camelot or Dead of Winter: we are all trying to achieve a common
goal, but one of us may secretly be working towards a different end.
I've played these a little but I've found that I don't enjoy them
much; I prefer a purer social deduction game like The Resistance.
(Oddly, while Homeland fits this pattern I enjoy it rather more;
there are two sorts of "honest" player role, the glory hound and the
one who doesn't care who gets the credit as long as the job is done,
and adding the possibility of a mole into that feels more reasonable.)
A Touch of Evil (and the old GDW game Minion Hunter) have no
traitor, but in its default play mode you each want to get the credit
for killing the monster, but can't do it alone, so you end up
switching between helping and sabotaging each other; I prefer the
optional fully-cooperative mode in A Touch of Evil.
That model might be extended into a prisoner's dilemma problem: we can
all win together, but if only a few of us go for individual victory
we'll do better, but if too many of us do that we'll all lose.
At the far end of the scale is something like Pandemic or my
long-term favourite Flash Point: we are all working together, we all
win or lose together, and there is no individual glory to be had.
I like games all over this range, but I like them to be clear about
what they're being, which I think may account for my general dislike
of cooperative-with-traitor.