Though both the designers work on web applications there are some slight differences in their work. Basically, the UI/UX designer only works on the look, design, and feel of the product whereas the website designer works on the entire design of the product they even need technical experience whereas the UI/UX designer doesn’t need technical experience. Both are booming careers if you are a beginner thinking to start a career as a designer then it is better to go with UI/UX design. For that, if you are looking for online training then I recommend you take up this UI UX design course from Intellipaat.
Before that do check out this Intellipaat complete UI/UX free tutorial video -