You are missing something. There is no such thing as STV 'under a single winner per constituency model'. STV is a system for deciding winners in multi-member constituencies.

There are two main axes for voting systems -- preferentiality and proportionality. STV is both preferential and proportional. AV is preferential but can't be proportional because it's for electing single members. First Past The Post is neither preferential nor proportional, and the bloody stupid d'Hondt system we use for European elections is proportional but not preferential.

This is not a matter of semantics. In AV you're voting for a single representative, in STV for multiple representatives. In AV if one candidate gets over 50% on first preferences that's the end, in STV preferences continue to count until all members have been elected. STV produces proportional results, AV exaggerates swings. They're similar in that the voter gets to rank candidates by order of preference, but the process of counting, and the results, will be wildly different.