Hey @STAGfm, welcome to the Processing community!
The confusion is very common, even I faced the same while I started to learn programming.
Nope, Processing and p5.js are NOT the same. p5.js has a similar structure to Processing just because it was meant to be a direct port of Processing in Javascript(this explains why both have setup and draw parts).
The main point of difference is that Processing is an environment based on the Java programming language while p5.js is a library based on the Javascript programming language (also note that both Java and javascript are not even reomotely related to each other even if they share a same part of their names).
In a sense, Processing will help you a lot if you want to build visual and interactive local applications where you want to import some Java library or work with Python. Processing would be helpful too if you want to perform serial communications like those with Arduino.
With Processing, you will be able to make your own .exe files which can run locally on your OS.
On the other hand, p5.js is not standalone. It is a JavaScript library. That means in p5.js, you will actually be coding in Javascript.
Processing comes with a full-fledged IDE to work with while p5.js has an online editor. The p5.js web editor is easy-to-use. Since p5.js is a JavaScript library, you will have to run p5.js sketches online on a browser only(Javascript also runs in Node but p5.js is a visual library).
With p5.js, you will be able to make visual web applications which can run only on browsers.
If you want the newest one, p5.js would be your best bet. JavaScript is the most booming language today and provides a wide range of updated resources (like libraries related to AI, ML to name some). Javascript is also easier to learn as a beginner because it is a dynamically-typed language.
But you should match your interests with what you intend to do with programming, and subsequently choose to learn any one of the two.
Tbh though, learning anyone of them will help. Both are very similar structure-wise. If you master one of them, the other one will look different only while reading the syntax.
I hope this helps and I could explain this properly.
You can refer to an article to clear any further confusion: Which Processing should I use? - Happy Coding