Legally speaking, British people are subjects, not citizens.
In 1983, the status of CUKC was renamed to British citizen (for those CUKCs resident in or closely connected with the UK: the situation in the remaining colonies was more complicated). At the same time, the status of British subject was officially restricted to those few British subjects who didn't qualify for citizenship of the UK or of any other Commonwealth country in 1949, and who were formerly known as "British subjects without citizenship".
So we are officially and legally citizens, not subjects.
Right to vote was already established before the change of the name (subject->citizen).
So, what changed? Well subjects have “privileges” that are afforded from the monarch, and citizens have “rights” which are given from the state.
Except:
1) In olde english law, the monarch and the state are literally the same thing.
2) Rights seem to be pretty loosely followed if they’re actually, you know, RIGHTS, and not privileges afforded from the state.
I’d say that semantically the difference is how the words make you feel, not the actual applicability of the terms to anything that has been realised.
But of course, citizens typically also have duties -- commonly, the duty to take up arms to defend the state -- and subjects can legitimately expect a reciprocity of obligations from the sovereign (e.g. the enforcement of the "King's Peace"), which sounds quite a bit like rights to me.
(All of which is a verbose and not very coherent way of saying that I agree with you.)
