this might be a vague answer since they are both really similar.
Cell differentiation is the process that causes unspecialised cells (so stem cells and all that jazz) to transform into specialised cell types with distinct functions and functions (nerve cells, root hair cells, muscle cells etc).
Cell specialisation is the unique features and functions that allow cells to perform specific roles within an organism. (so the neurons and stuff on nerve cells etc).
So the difference would be that cell differentiation is actually just the process that makes stem cells into proper cells but cell specialisation is what makes them do their job.