"UX is not UI" is a widely discussed topic by those who practice UX and see visual designer / user interface designer use the term. I myself sometimes want to reach through the screen when I see someone comment "Awesome UX" on a static design on Dribbble.
UX has, to some extend, become a "hipster" term that some companies use without really knowing the extend of what UX is.
User Experience is a very broad term. Visual Design is just a part of the entire umbrella. My experience is that companies asking for a UI/UX person, want a designer that can do a little more than just "make things pretty". A person that can take a concept, help determine the requirements and design a useful and stylish application.
But answering your questions:
A UI designer is a graphical designer specialised in designing user interfaces for digital products. You're required to be creative and capable of creating the right (as in fitting) design for a product or company. What your exact tasks would be depends on the company. Is it an internet bureau that does client work? You'll probably help build concepts from the ground up. If the company has it's own product, you'll probably help improve and expand the product. In bigger companies you'll probably be a tiny spil in a bigger engine. Just designing stuff and delivering your work to the next person. In smaller companies you might have more influence on the project. But this differs from company to company.
You'll be using visual editing software, which is anything from Adobe: Photoshop, Illustrator or the more recent Adobe XD. Sketch is also very popular.
An Interaction Designer is more concerned with the flow of a product and if it's usable and accessible. They design with the user in mind (user centered design). They find out what the user wants to achieve and come up with the best solution. They substantiate this with research done by others or they even play around with user research themselves. Some interaction designers just make wireframes and turn those over to the user interface designers. Other interaction designers also know how to make something pretty and are proficient in the editing software mentioned above. For wireframes, you can also use dedicated software like Axure. I personally stick to pen and paper, at least at first.
Like I mentioned, there are companies who don't know the extend of what User Experience is. I believe this is mostly a combination of UI and UxD. That is, without the user research primarily. But you could add easily add a bit of user research in your work.
With a background as a web developer you could be very valuable to a smaller company. Some might call you a unicorn. In the first stages of a project you bring technical knowledge with which you can say what is technically possible. It can boost creativity and prevent ideas that are impossible to create (at all or within the budget).
And as for not being a graphic designer, it was Picasso who said.
Good artists copy, great artists steal