I’ve always heard that a majority vote was 50% plus one vote. Is this correct?
No. A majority is simply “more than half.” For instance a majority of 22 is 12 (more than 22 divided by 2; greater than 11) but a a majority of 21 is 11 (more than 21 divided by 2). By using the 50% plus 1 rule the majority of 21 is either 12.5 or 13, depending how you treat rounding. See RONR10 p. 4 & p. 387.
You may also hear persons (especially newscasters) use the terms “simple” majority or 2/3 majority. By using the term “simple” the person is trying to convey that only a majority vote is required. When they use the terms 2/3 majority (which is inconsistent: either you want a majority vote — more than half — or a two-thirds vote — at least twice as many on one side as the other) they are trying to convey — albeit incorrectly — a larger vote than a majority, also known as a “supermajority.”
See RONR11 Chapter XIII §44 (pp 400-405) for a further discussion regarding different bases of votes.