You can apply Z-scores on whatever you want, but it must make sense and depends on what you want to do. What is the context? See for example Scaling RNA-Seq data before clustering?
Typically though it is applied to data on log2 scale because without log2-transformation standard deviations, hence Z-score range is very large and probably meaningless.
logFCs are a bit difficult to cluster I think, because fold changes without stats attached to it are meaningless. They can be very big, due to noise. I would cluster logcpms or vst. Not logFCs.
Difference is that plotting Z-scores plots each group and logFC plots differences between groups. Simply a different way of showing things. Depends on what you want to show.
I made this. Z scored on log2FC? will anyone support me on this?
3 groups A,B,C