Q: Does the word "know" mean the same thing in "I know him under a different name." and "This flower is known as a Peruvian Lily."?

A: the same meaning

Q: Does the word "mouth" mean the same thing in "He rode into the mouth of the canyon." and "They built a fire at the mouth of the cave."?

A: the same meaning

Q: Does the word "see" mean the same thing in "I see that you have been promoted." and "We had to see a psychiatrist."?

A: different meanings

Q: Does the word "make" mean the same thing in "Don't make this into a big deal." and "He made a fool of himself at the meeting."?

A:
the same meaning