Undergrad Difference between Zero-Field Cooling and Field Cooling

[dwellexity]

I am currently doing a experimental project work on superconductors. I am supposed to study properties of FeTeSe.
I am having trouble understanding the difference between Zero-Field Cooling and Field Cooling. In both cases, I am measuring magnetization with varying temperature (from lower to higher) while a non-zero magnetic field is applied. Why does it make a difference whether I cool after applying field or apply field after the temperature has been lowered as required.

 

[f95toli]

FeTeSe is presumably a type-II superconductor, right?
What does that mean in terms of how it reacts to an applied magnetic field?

Hint: Look up some information about the formation of vortices in a textbook (see e.g. Tinkham's book)