I personally like to compare it to building houses.

Programming is laying the bricks, the cables, etc. Basically doing the actual building.

Software engineering as in other engineering disciplines is more concerned with making sure everything actually works and fulfills certain standards of quality. The planning, design and architecture part of the work.

For the last decades the person doing the programming and engineering were usually the same, but they are more and more drifting apart with more engineering focused roles like software architect.

In much of the world engineer is also a protected title that requires formal education like with doctors or lawyers. The US is using it pretty inflationary.