Note: There is no fixed distinction between ʁ, ʀ and r in German. Dialects heavily differ but they may also be mixed in one word and any of them is considered correct.
ʁ is described as a fricative version of ʀ, but this mostly applies at beginning of syllables
Ich ←→ Richter
Angst ←→ Rang
and after the b/p, d/t, g/k consonants pairs, where the ʁ inserts a "backstop" after the preceding consonant.
Band ←→ Brand
Buch ←→ Bruch (note: long u in Buch)
Pacht ←→ Pracht
Punze ←→ Prunk
Dach ←→ Drache
Deck ←→ Dreck
Tag ←→ trag
Gas ←→ Gras
Kasse ←→ krass
With the f most people would use rather a ʀ instead:
Fisch ←→ frisch
That is because this "backstop" ʁ is barely hearable after non-plosives. And that's exactly what you have after a vowel. Vowels are not plosives. The ʁ is barely hearable.
A common tongue twister plays with this:
Fischers Fritz fischt frische Fische. Frische Fische fischt Fischers Fritz.
Most people will give up because the name Fritz sounds weird when not pronounced with ʁ, while frisch "requires" the ʀ.
In addition, the very common German syllable ending -er is pronounced ɐ, so people often place this ɐ everywhere they spot a stray -er-.