@myself2020 eh?! A wedding is not up for definition! If you arent actually getting married - I.e. signing the papers - then it isnt a wedding, regardless of what people want to call it.
Actually it is up for discussion.
Until the late 1980s, early 1990s the only places you could legally marry were register offices and C of E churches (in England that is).
So ay one who got married i a Temple, Synagogue, Gurdwara etc had ro wither have a separate registry office wedding or have a registrar attend to sign that the wedding had taken place according to, the rights of RC church, Jewish faith etc.
Not everyone bothered with the legal side.
Everyone and his dog considered the bride walking down the aisle, the exchange of vows, the ring the wedding. Not the bit when the register was signed which often happened outside the church or in the vestry.
Lots of venues do not have a licence because then there are restrictions, they have to offer the venue for a number of years and you cannot have any religious music or prayers.
OP I think you need to find out how the mothers were told before you get angry at the celebrant.