Not even remotely the same thing. Not sure how you would not understand the difference immediately upon trying each, but Photos is a local application on your Mac that organizes and edits your images. It's library can be backed up as part of Time Machine or any other method you use to back things up. Photobucket is a website that provides a limited amount of storage for images (probably NOT at their original resolution, it should be noted), and offers extra storage for a fee along with other services for a price, such as making coffee mugs out of one of your photos and such.
Online services like PhotoBucket, Flickr, Amazon Prime Photo Storage, iCloud Photo Library, Google Photos and so on and so forth are useful in the sense of having an offline backup (again, however, check on whether they store the originals at full resolution: not all do), and in the sense of having a way to link those photos easily to other sites and services, like here, or on Facebook, etc.
There are some other advantages and issues, but that should give you a good overview. Let us know if you have any other questions.