The entries from LancashireBMD are from the lists of Birth, Marriage and Death Registrations within the County since 1837, and are prepared from the records held by the various Register Offices. These are being transcribed by Family History Groups to make them freely searchable via the internet. In the case of marriages those that appear within the lists show the venue, and from the information given for Thomas and Catherine's entry I would think that the venue was Manchester Register Office, rather than a church of any denomination - MCR RM is the code shown for Manchester Register Office.