KM,
Sorry, but I find myself at some variance with your definitions, as follows:
1. I am in broad agreement wrt "rest".From an Australian perspective, there is no doubt (latterly subject of course to the CASA Director's whim) that "rest" involves vacating the seat and making use of the "bunks or berths of a type approved by CASA". Although you might like to draw the implication that there must therefore be a replacement pilot, I think that from a legal perspective that issue is covered in diverse other places ranging from the Company Ops Manual to the rules for use of oxy masks.
2. However, the term "in-flight relief" is recognised in quite a different way from that you espouse. As I think it is not yet defined in a regulatory sense, the dictionary definition is a guide. Three successive definitions from the World Book Dictionary give us: "freedom from a post of duty, often by the coming of a substitute"; "a change of persons on duty"; and "a person or persons who relieve others from duty". That is to say, "in flight relief" is the process whereby one is replaced in the chair.
As far as I am concerned, this is the other part of the picture, and if you would take a look at the draft Part 121, at Appendix 1 to 121A.940, you will see the proposed rules for in-flight relief. Amongst other things, it calls up "another suitably qualified flight crew member", and further spells out certain requirements for relief of Captains, and so on.
It may be, of course, that in some far-away land, some regulator has allowed (or has been over-ridden by vested interests) the definition of "relief" in some other way. If that is the case in your employment, you have my sympathy.
Xmas Wishes
Gru