UX, UI, Usability - how not to get confused by the trendy words

UX, UI, Usability - these words are commonly used along with the phrases "good product, usable system, happy user". Most of us are hearing, using and even improving these things in our everyday routine. 

Have you ever thought deeply about these terms? What's the difference, and what's common? 
"This is obvious" - you might think. However, it's not so clear if you think from the top of your head. Very easy if to check deeply, though. What mistakes do we make talking about UX?

Key points:
- what's UX, UI, Usability; differences and similarities
- examples and mistakes of usage
- UX and UI designers: who are they and what are they doing?

Target audience:

- Anyone who is not expert in UX/UI design and usability
- Anyone who uses or wants to use these concepts

You will not get confused by all the words starting with 'U' any more.