I also found it a bit difficult to follow along with the branding of Spotify. So I will try and help to layout out some solid ground work to get you started.
The Spotify logo is a custom font called "Spotify Lagom Bold and it’s a tweaked version of the typeface Akkurat" 2
They also use a hand sketch font that is custom and it sort of looks like Sketch Block. The same font I used in the title.
You can find other fonts on their UI Guidelines page.