What's the difference between mouser and muser?

Mouser

Definition:

• (n.) A cat that catches mice.
• (n.) One who pries about on the lookout for something.

Example Sentences:

Muser

Definition:

• (n.) One who muses.

Example Sentences:

• (1) It takes in the Greek and Roman idea of the muse as source of the artist’s inspiration as well as the French “muser” – to meditate or waste time.