I consider the s p d f orbitals as a subshell, but I have heard about the term sub-subshell. what is the difference between these two?
As you pointed out the the s, p, d, and f denoted subshells of atoms.
The term sub-subshells is very uncommon. I did find a couple of uses.
Materials Science By G. K. Narula, K. S. Narula, V. K. Gupta
pdf file about Modern Atomic Mechanical Theory, page 24
What the authors are noting is that the 2p subshell will have three orbitals which can support two electrons each. Each of these three orbitals is being referred to as a sub-subshell.
As I said it seems a very uncommon term, and I'd suggest you avoid using it.