What is the difference between a PhD degree and a DSc degree?
It depends on the university and the country.

In England, a PhD is typically awarded for a thesis and oral examination of the thesis, usually followed by implementation of corrections to the thesis, the requirements for which are specified during or just after the oral exam. It's often done soon after a Masters, which is done soon after a Bachelors, so a fairly large proportion of PhDs are awarded at the start of one's academic career. Whereas a DSc is awarded for a portfolio of work, (in some cases submitted together with an over-arching critique of that portfolio), and thus is more likely to be awarded later in an academic's career.

Nominally, a PhD is a doctorate in philosophy, but is typically awarded for pretty much any subject. There are some who argue that philosophy of knowledge always form part of these studies, regardless of the subject. I occasionally use this line to try to inspire students, myself. A DSc is a doctorate in science, and is not awarded for literature, law, divinity, or music, each of which has its own dedicated higher doctorate. 

The DSc is a higher doctorate than a PhD, in England. In some other countries, they're equivalent.

Both get the honorific title doctor.