I am currently using Wattpad to work with because I really like the website layout, format and the community. It's a very positive and fun place. However, is it really considered self-publishing? I'd like to think so, but on Wattpad you do not make a profit from your works. Has anyone else used this site? If so, how has it worked for you? If it hasn't worked for you, what could you tell me about it? I just don't want to mess up. What I mean is, I don't want to have a successful story on Wattpad that I could've done more with. You understand what I'm saying? I understand I have a lot to learn, but I'm looking into self-publishing as a way to get my works out there.
I would say it's publishing, and you're doing it yourself, so... self-publishing! But in terms of getting your work "out there" you may want to consider self-publishing through Amazon, maybe especially Amazon Prime. I guess it will depend on why you want your work out there - are you trying to build an audience in general, or are you trying to build an audience that will someday be interested in buying books from you. I think the Wattpad crowd can be excellent fans in terms of out-there-edness, but I'm not sure you can count on them to translate to book sales (they're already pretty happy with the free books they're reading on Wattpad, after all, so why would they start paying?). So if you want an audience that will eventually buy your books, you may want to start with an audience that has shown more of a willingness to pay for books, and the biggest bunch of that crowd are on Amazon. You'll have to charge for your books (at least 99 cents) most of the time, but if you're in the Kindle Unlimited program you can get occasional free days and if you're in Amazon Prime readers won't have to pay for your books independently, they just pay an monthly fee for access to loads of books. I won't go into more detail since I'm not sure you're at all interested in this, but if you are there are lots of people on the forum who are publishing through Kindle - they can help you out.
I would say short stories can go on Wattpad, but if you write something novel-length, monetise it through Amazon. Even if you release all your short stories on Wattpad, that doesn't stop you publishing them as a collective work on Amazon. As Bay View says, the audience on Wattpad probably aren't your customers on Amazon. Anyone spending any significant amount of time reading things on Wattpad isn't going to want to pay money for books.
Honestly, I used Wattpad early on in my career thinking it would be a good idea to get "exposure", and while it did get some good attention at first, it stinks when it comes to monetization. Basically, I'd use it as a place to maybe put some snippets of larger stories, and direct them to your Amazon or other self-publishing pages, even patreon if you have one. But otherwise, market yourself on other social media websites such as twitter and stuff first. It helps a lot better when ti comes to making money.