"Is there any difference between “span in line” and “span in plane”?"

Yes.

Think of span as "how far can something stretch".

If you stretch a line it is different to if you stretch a plane.

The span of a line just means all points on the line from -infinity to +infinity.

The span of a plane means all points in a plane with 4 corners that go to +/-infinity.

If the line lies within the plane then the span of the line is a subspace of the span of the plane.