Yes, on a plane surface (a flat sheet of paper, for example).
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The shortest distance between two points is... a straight line.
A straight line is the shortest distance between two points, a line is the delineation of a connection between two or more points.
Without wishing to overcomplicate matters, one could simply define a straight line as: "the shortest distance between two given points".
In plane geometry it is a straight line. If you want to know the shortest line between two points on a globe, it will be the intervening section or arc of the great circle route that connects the points. The great circle will be a circle that cuts the globe into exactly equal parts, like the equator.
You get a curve. If you join them along the shortest [Euclidean] distance between them, you get a straight line.