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

The word "kerosine" is a variant of "kerosene".

A variant of the same word.

A: the same meaning

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

It is not known who created this piece.

She played two beautiful pieces on the piano.

A: different meanings

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

Gather some stones.

If you want to emphasise the shape, it is possible to gather the waistline.

A:
different meanings