It's that, but there's a lot more. It's simply very, very slow and seems poor at managing memory. It's difficult to describe, but things that used to respond very quickly (like scrolling between pages on the home screen) are slower than just "sluggish". And often apps don't behave well if I have more than a couple of them open. But it's not all the time, it's just frequent.
Then there is the problem where it doesn't rotate properly. And my first instinct would be to blame the hardware, but in the case of Messenger, it rotates some parts of the screen and not others. But the parts that don't rotate are unresponsive. So I'll sometimes find myself in a situation where I've typed a text, and the message is rotated, but the text box and send button are not, and pressing the send button does nothing until I manage to get the entire thing to rotate by moving it from landscape to portrait and back a few times.
It's also possible there is some cruft I've carried over from previous version (I've upgrade a few times) so I'm going to try a 'fresh' install where I lose all my data and have to redo everything by hand and see if it fixes the problems. But the only problem I had prior to installing iOS 9 was my music not transfering properly, and AFAICT, that is an iTunes problem relating to duplicate tracks that I haven't had time to resolve yet.
If it's not the cruft, I guess I take it back and get a "new" one; maybe a problem with the RAM?