Here "engagement" as a celebration is something you had in the 50s or 60s. After that you did not get engaged -you just married. Both people picked up their rings together and they were simple bands in yellow gold. Very avantgarde people (like me when I married first time in 1975) wore no rings at all.
As times passed the wedding bands became more eleborate. And within the last ten years the US fashion has taken over, fuelled by TV shows I suppose. Now women - especially of the more wealthy classes- get that 3-salaries-diamond for engagement and wear it with the wedding band later.
Very old-fashioned people (like me when I married the second time ) don't wear any wedding ring.