So I have two responses to the main post and one follow up comment that has not been brought up yet. My opinion is that if we want to distinguish between the different kinds of reliability, then yes, we should have separate tags.
1) Reliability Theory actually has two different definitions (general statistical reliability and educational reliability). The latter reliability is more biological in that it is specific to psychology, teaching, education, and a few biological fields: https://chfasoa.uni.edu/reliabilityandvalidity.htm
I am not sure how the tagging process works, but it probably necessary to have more than one tag we can distinguish the different definitions of reliability. After posting this I realized that there is more than one tag.
2) Inter-rater reliability is a type of statistical reliability and a part of reliability theory. I personally think all inter-rater reliability questions are also reliability questions, but hey I don't know everything. So at least for me, reliability indeed leads to some misinterpretation if we are trying to keep questions about reliability and inter-rater reliability separate.
A heads up about reliability:
3) There can be a cross-over between educational reliability and statistical reliability. Here is a very specific recent research example involving Bayesian Statistical reliability:
https://arxiv.org/abs/1404.3656 . I know no other specific examples; however, so the cross-over would be very narrow on StackExchange to questions about applying better math to grading in education. I would imagine this means that there should be some kind of reference or link in the question if the two are mixed. This is of a heads up statement for the mods and administrators rather than something actionable, as I can find little examples of this happening in the stack-exchange (but there could be deleted posts I don't see).