When you do Edit>Stroke selection the selection is "suspended" and the stroke straddles the selection boundary (more accurately, the line that separates pixels with Selection<50% to those where Selection>=50%) so in practice the stroke extends outside the selection.
When you do Select>To path followed by Edit>Stroke path (which is usually cleaner), the selection is not suspended, so if you don't do anything you only get the part of the line which is inside the selection. To get a full line width straddling the selection boundary you would have to remove the selection before the stroke step (you can save it to a channel if you think you'll need it later).
When you do Select>To path followed by Edit>Stroke path (which is usually cleaner), the selection is not suspended, so if you don't do anything you only get the part of the line which is inside the selection. To get a full line width straddling the selection boundary you would have to remove the selection before the stroke step (you can save it to a channel if you think you'll need it later).