I know people who spend their whole life together in a committed cohabiting relationship and some raised children together etc They just didn’t want marriage (or couldn’t legally marry. It’s perfectly great. But then they never claim to be engaged or refer to each other as fiancée. They call each other “partner” or “life partner” or some other more appropriate term. Maybe in places where common law marriage is legal you can say you are actually married if you cohabitated long time. Still not calling each other fiancées.
And I’ve met some people who call themselves engaged or if broken up they call the person “ex fiancée” just because they casually discussed “what if we get married one day”. Or the woman just bought herself a ring and called it engagement to a random person.
Some interesting situations.
In my understanding engagement means acknowledgement to ourselves and the families and friends that we will be getting married and then get married.
I think sometimes people call things certain way because they have wishful thinking about something, but it’s not really what it is