M.D.
I did some research on this last year before Christmas, and this is what I was told at that time...
They provide very similar functionality but ONLY when they are talking to a phone of their same operating system. So, for example, you can answer calls, respond to texts, get calendar alerts, and see push notifications from your iPhone apps on your apple watch. Same for android watch and android phone. However, the apple watch can't communicate with the apps on an android phone.
They say on the android watch box that you can sync android watches to an iphone and that is true for the call feature (as far as I know), but this is somewhat misleading. I was told that it can't talk to any of the apps, so none of the push notifications, texting, etc, would work. There are some workarounds for this, apparently, but it's definitely not as straightfoward as when the watch and phone are matched. So, functionality is limited if your watch and phone are not matched in terms of their operating system. (Apple doesn't even pretend. They straight up say no, their watch will not pair with an android phone and they don't make any kind of work-around app to try to change that.)
As to what functions the apple watch can provide when paired to an iphone - it depends on the version. The less expensive ones communicate with the phone to answer calls, respond to texts, receive notifications, etc, when your phone is within bluetooth communication distance. They also have fitness tracking. The more expensive apple watch has its own sim card, so it can do all of those things and you don't even need to have your phone with you (of course you have to add the watch to your wireless data plan), plus the more expensive one is water proof and the less expensive one is not.