If it was me I would be ringing the restaurant and asking if they have a set price for this wedding and what is on the menu. Does this include drinks.
My mum went to a birthday dinner awhile back and it they were asked to pay for their meal after they had eaten. She was not impressed and thankfully had just enough cash on her.
I think invitations should have clear details if they want their guests to pay their own way. This should have who is invited, the costs involved and menu.

How many people have cash in their pockets these days and some places don't like you paying by card when the bill is split.