Q: Does the word "focus" mean the same thing in "Please focus on your studies and not on your hobbies." and "Focus on passing the test."?

A: the same meaning

Q: Does the word "left" mean the same thing in "The political left is not holding enough power." and "Jab with your left."?

A: different meanings

Q: Does the word "catch" mean the same thing in "Did you catch a cold?" and "The fashion did not catch."?

A: different meanings

Q: Does the word "look" mean the same thing in "He went out to have a look." and "His camera does his looking for him."?

A:
the same meaning