Q: Does "take" have the same meaning in the following two sentences?

I'll take three salmon steaks.

We are taking an orphan from Romania.

A: the same meaning

Q: Does "trace" have the same meaning in the following two sentences?

Trace a pattern.

Trace the student's progress.

A: different meanings

Q: Does "beg" have the same meaning in the following two sentences?

I beg your pardon. I didn't mean to cause offence.

I begged to come.

A:
the same meaning