I find it interesting that, although Law 12 is called fouls and misconduct, "foul" is never defined. I suppose there is something implicit from the titling that all that is not misconduct is a foul, which would make handling a "foul." I seem to recall that before the great rewrite of the 90s that Law XII referred to what are now DFK offenses as "penal fouls," and that included handling. But I don't have my old books handy--I'll take a look when I get a chance. I think the reality is that the usage of "foul" is inconsistent--in some of the places it is used it seems to include handling (e.g., signals for whether a foul occurred in the PA) and in others only to refer to the other DFK offenses.
In the US, it is true that foul has generally been used as including handling. The classic definition was a foul is committed (1) by a player, (2) against an opponent (or the opposing team in the context of handling), (3) on the field of play, (4) while the ball is in play. That definition has taken a beating in the past few years with fouls occurring off the field of play and certain fouls being against any person.