Nitpicking: a more correct view is that the set of points on a straight line is an affine space, so the points are neither scalars nor vectors, but elements of an affine space.
The set of translations of the straight line is a vector space a.k.a. a linear space.
So the vectors are the classes of equivalences of the differences between 2 points on the straight line (i.e. the differences between 2 pairs of points, where the distances are the same, are equivalent and they determine the same vector).
While the vectors are classes of equivalence of the differences between 2 points, the scalars are classes of equivalence of the quotients of 2 (collinear) vectors, i.e. a scalar is the ratio between the signed magnitudes of 2 collinear vectors.
If you choose a point on the straight line as the origin, you can choose as a representative of each class of equivalence that corresponds to a vector, the vector corresponding to the origin point together with another point. This gives a bijective mapping between vectors and those second points.
If now you also choose a vector as being the unit vector, which will correspond with a second point besides the origin point, together with the origin point, then you can choose as a representative for each class of equivalence corresponding to a scalar the ratio between a vector and the unit vector, which will correspond to a third point, besides the origin and the point corresponding to the unit vector. So you obtain a bijective mapping between scalars and those third points.
Because on a straight line there are bijective mappings between points, vectors and scalars (after choosing 1 origin point and a 2nd point as the extremity of a unit vector), they can be used interchangeably in most contexts, but it would be good to remember that all 3 are in fact different mathematical entities.
The set of translations of the straight line is a vector space a.k.a. a linear space.
So the vectors are the classes of equivalences of the differences between 2 points on the straight line (i.e. the differences between 2 pairs of points, where the distances are the same, are equivalent and they determine the same vector).
While the vectors are classes of equivalence of the differences between 2 points, the scalars are classes of equivalence of the quotients of 2 (collinear) vectors, i.e. a scalar is the ratio between the signed magnitudes of 2 collinear vectors.
If you choose a point on the straight line as the origin, you can choose as a representative of each class of equivalence that corresponds to a vector, the vector corresponding to the origin point together with another point. This gives a bijective mapping between vectors and those second points.
If now you also choose a vector as being the unit vector, which will correspond with a second point besides the origin point, together with the origin point, then you can choose as a representative for each class of equivalence corresponding to a scalar the ratio between a vector and the unit vector, which will correspond to a third point, besides the origin and the point corresponding to the unit vector. So you obtain a bijective mapping between scalars and those third points.
Because on a straight line there are bijective mappings between points, vectors and scalars (after choosing 1 origin point and a 2nd point as the extremity of a unit vector), they can be used interchangeably in most contexts, but it would be good to remember that all 3 are in fact different mathematical entities.