What's the difference between otiose and otiosity?

Otiose

Definition:

• (a.) Being at leisure or ease; unemployed; indolent; idle.

Example Sentences:

• (1) I called the hospital and asked why my GP would have made such an otiose request.
• (2) In the circumstances, comments by analysts that the data was "not good" and "seriously bad" were somewhat otiose.

Otiosity

Definition:

• (n.) Leisure; indolence; idleness; ease.

Example Sentences:

• (1) I called the hospital and asked why my GP would have made such an otiose request.
• (2) In the circumstances, comments by analysts that the data was "not good" and "seriously bad" were somewhat otiose.