What is the difference between the medical terms "paresthesias" and "dysesthesias"?

Itching versus pain. Paresthesias refer to abnormal sensation "numbness and tingling" which can be annoying. Dysesthesias are a more intense version of the same sensation which you would call painful. The sensations run on the same nerve endings, again one is just more intense than the other.
Good question. Paresthesia means altered sensation, not necessarily disagreeable. Dysesthesia means altered sensation which are disagreeable (especially painful). All dysesthesias are paresthesias (but not the other way around).