As far as I can tell, that's the case. For some events at some dates there do appear to be registers for St Mary's, but I think the entries are also duplicated in the St Peter's ones.
I have an ancestor who died in 1835 and his burial is recorded in the St Peter's (the ancient parish church) registers as being at St Mary's. On the Yorkshire Burials website there are two entries for him - one at St Peter's and one at St Mary's (which they call St Mary's, Mabgate). That was a new discovery for me today, but I haven't worked out whether that means I need to look for another register entry, or whether the St Mary's entries have been extracted from the St Peter's dataset and merely presented as if they come from a separate register.
However, Yorkshire Burials also have a transcript of a memorial to him at St Mary's (also new to me
), which I think is fairly conclusive. You can be a bit unsure what words in a register refer to, but it's a lot harder to make a mistake about which churchyard you're recording MIs in.
