What's in a Name? Kazimir versus Kaz versus Kaziu

Hello All ... Kazimir versus Kaz versus Kaziu. What the difference & is Kaziu more friendly like calling Frank Frankie?

Kazimierz [ka-zhi-miezh] formal
Kazik [ka-zhik] pet-name
Kaziu [ka-zh-yu] - vocative case of pet-name

In some dialects the vocative form is used in the nominative: Jasiu przyjechał, Stachu jest przy forsie, Kaziu kocha boską Isabel...etc,, itd., itp.

Kazimierz is formal, right.
Kazik is a pet-name
Kaziu is _not_ the vocative of Kazik (which would be Kaziku) it's the vocative of Kazio, another pet-name.

In standard informal spoken Polish the vocative can be used a nominative but this only works for pet-names for men/boys where the vocative ends in -u, when the vocative would end in -(i)e you can't do that and if it's not a pet name you can't.

Leszku could be the vocative/nominative for Leszek as a petname for Lech but not for the separate man's name Leszek.