No, all kites do not invert equally, there are huge differences.
Kite inversion means the kite goes inside out wind on the top surface, with a lot of stress on the struts now.
Not to be confused with line inversion where the kite just tumbles through the lines so they are crossed, no biggie and can happen often depending on your style.
Inversion tendency is almost every designers nightmare, as it has not been so easy to predict for some reason.
Underinflation will of course accelerate this tendency, but that is outside the topic.
There ARE kites that are a lot more likely to invert than others.
Big or small kites do it.
When powered to the upper limit and very depowered and then loaded t.ex flying/diving the kite, those prone to inverting can do it, quite scary when it flaps like a stingray suddenly, or might even yank down in an uncontrolled loop.
These are typically the ones that tends to invert easier when they tuck down forward or roll on the water.
I have seen ONE kitesize in a line do this more than the others, at several brands, especially earlier years - so I think they have an idea what is causing it since we see it less often now.
Apparently Slingshot has a bad reputation in this thread, have no experience myself with these and could also be earlier years maybe?
Think it could be a coincidence they are mentioned I dont know, as there ARE kites that do it more often than others, amongst many many brands through the years IMO.
Here is an old clip with an example - it seems underinflated and could be the reason but the principle is the same for those prone to inverting.
Difficult to see as it starts outside the view - but what happens is the kite inverts in high winds when dived starting and becomes a live pretzel
Inflating rock hard, if you got one with this tendency, can usually stop this from happening.
You somehow treat the symptoms this way, not the disease and root cause, but it works quite well
Great that newer kites seem to have lost this tendency