I can only speak about my own experience of what Wild Swimming is to me and my journey with it.
It seems from reading through some comments that there is some resistance ( not sure why ? maybe one for some internal rhetoric and reflection?? ) to the term ' Wild ' with a fair few older'n'bolder folks seemingly stating they swam without the requirement for semantical differences when they were younger - If so I applaud you - as long as its not just some nostalgic 'we had it hard in my day' type imagined version of past living.
If the issue is the term - 'wild' just think of it different as the normal lane swimming in purpose built swimming pools - lets call that 'Urban' Swimming and just decide they are different flavours of the same thing.
To ME urban swimming ( Indoor pool , beach holiday , waterpark ect ) IS different to what Wild swimming is - there is no spiritual ( stick with me people - I'm not a hippy ) connection to nature .
Evening dipping into a river or pool on a warm summers day I would say is more akin to urban swimming than what most people will regard as Wild Swimming. Swimming in that situation is more fun and a social past time.
Wild swimming I think is in some ways more a cathartic reconnection to nature and oneself. Its a challenge and it tends to be more a discipline than an activity of enjoyment.
In my journey with - I'll call it swimming outside so people don't get triggered - I've swam in a massive variety of places and visited a huge range of places I would not have visited or swam in without trying to expressively experience it.
Swimming alone - reconnecting with nature .
So yes - I do think there is a difference. IMO.
Arctic Circle