In English bridge terminology, the term "limit bid" meant (and in some circles still means) a non-forcing bid which shows the strength to bid to the level at which you're bidding, and no more. It was used to apply not just to three-level raises, but to any raises, notrump bids, rebids of one's own suit, etc. Such bids were, as others have mentioned, a defining charactistic of the Acol system.
All of these would have been described as "limit bids":
1♠-1NT showing less than an invitation
1♠-2NT invitational
1♠-2♠ showing less than an invitation
1♠-3♠ invitational
1♠-4♠ showing enough for game but no more
1♦-1♠;2♠ showing a minimum
1NT-2NT invitational
The idea was to distinguish from the style where sequences like 1
♠-2NT and 1
♠-3
♠ were forcing. Even if these are limited, they don't involve bidding to the limit of one's strength.
In the English usage, a "limit raise" was simply a "limit bid" which is also a raise, so 1
♠-2
♠, 1
♠-3
♠ and 1
♦-1
♠;2
♠ were all "limit raises". To describe a raise which was invitational, one would use the phrase "invitational raise".
I'm not sure why the North American usage is different, but I think it's fair to say that it lacks logic and is less useful. In England one now encounters both usages, so that the term "limit raise" is now so ambiguous as to be useless.