Question: "stay" used in the same way in the following two sentences?

I had to stay at home and watch the children.

After the trial period, she was asked to stay on and work full-time.
Answer: different meanings
Question: "admit" used in the same way in the following two sentences?

This ticket will admit one adult to the show.

This pipe admits air.
Answer: different meanings
Question: "fall" used in the same way in the following two sentences?

Fall into a trap.

Fall in love.
Answer: the same meaning
Question: "serve" used in the same way in the following two sentences?

This table would serve very well.

His freedom served him well.
Answer:
the same meaning