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

He gave notice two months before he moved.

He took no notice of the changes, and went on as though nothing had happened.

A: different meanings

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

We'll have to shift these boxes to the downtown office.

Shift one's attention.

A: the same meaning

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

Can you back up your claims?

I can't back this plan.

A:
different meanings