Each manufacturer loads the phone with their own 'flavor' of Android so to speak. They put some of their own stuff on top of the Android OS. I know for my Motorola ATRIX I have 'MotoBlur
'. HTC has their 'HTC Sense' I believe and Samsung has 'TouchWiz'.
Each of these custom UI's have different features and so on like the widgets you described.
Regarding the clock and weather widget that you described I think you can easily create that using the app 'Beatiful Widgets'. You can get that from the Android Marketplace.
The beauty of Android OS though is your free to do what you want with your phone in terms of customizations. Once you root your phone, which is relatively simple, you can load up custom ROMs that devs cook up. These ROM's have tons of different themes, features etc. It doesn't just stop with the look of your phone either. There are tons of mods too like for instance I can start up my phone with the volume button if I like instead of the fingerprint scanner. Visit XDA for all you need to know on this stuff. Great resource!