There's also some differences between the mechanics of them as immortals between the original movie and everything else.
In the movie, after Connor awakens as an Immortal, he can't die -- getting stabbed hurts, but that's it. He can't swim, but he can walk across the bottom of a lake no problem.
From the second movie on, if an Immortal takes lethal damage, he or she "dies" then regenerates soon after.
I'm reminded of a video game they announced years ago, where one of the mechanics was going to be that you could disarm enemies of their melee weapons by letting them run you through and just leaving the sword or knife stuck there while you disengaged.
Shame it never got finished (or, for that matter, started beyond the announcement).
And I'd be fine with never knowing the reasoning behind the quickening and immortality. That being a mystery was part of the original movie's charm.