You shouldn't think of the watch as a separate device, It's a second screen for the phone you're setting it up with.
it is a different number, but you will never see that number unless you really go looking for it. All Calls and messages will go to and from the number of the phone. (or however your phone is configured, like iMessage email address). I had to go to my account page on the t-mobile website to find the number, sending a text to that number did not do anything.
your watch should be paired to your phone. Your wife's watch to her phone. If you use your phone to set up a watch for her, it will receive all of the calls, messages, and notifications from your phone. you can not assign a different apple account to a watch.
There is a small exception to this. You can set a watch up for a family member, but will loose a lot of functions. This is designed so you can give a child a watch without them having their own phone. The watch must be cellular model.
https://support.apple.com/en-us/109036
An Apple Watch for someone with an android phone is pretty much useless. You'll have to jump though a lot of hoops to make it work, and even then it will be severely limited.