I'm gonna try and give a short answer here but one key thing to say is that the answer to this question will be different from designer to designer!
Every designer has methods and concepts they favour and these are mine, it's kind of like when devs have favourite programming languages or frameworks haha! :D
These are more UX:
Human-Centred Design (HCD) or User-Centred Design (UCD)
Participatory Design (Methodology)
Liberatory Design (Methodology)
How to conduct user interviews
UI:
Understanding design systems and how those work/compliment UI frameworks like...Ionic for example.