Q: Does the word "day" mean the same thing in "It should arrive any day now." and "These days it is not unusual."?

A: the same meaning

Q: Does the word "mouth" mean the same thing in "They built a fire at the mouth of the cave." and "He stuffed his mouth with candy."?

A: different meanings

Q: Does the word "counterfeit" mean the same thing in "To counterfeit the signature of another, coins, notes, etc." and "They counterfeited dollar bills."?

A: the same meaning

Q: Does the word "dip" mean the same thing in "Dip the brush into the paint." and "I had to dip into my savings to buy him this present."?

A:
different meanings