Vectors in general sense (Calculus, Physics, etc) are physical quantities such as force, velocity and displacement, that have direction and magnitude. Directed line segments (with no particular position) are used to show vectors. Such directed line segments (rather than the physical quantities that they represent) are themselves often regarded as vectors. Two directed line segments are regarded as the same vector, irrespective of their position, as long as they have the same direction and magnitude. In that general context, when we do try to use vectors for determining/identifying points/positions (for example, vector equations of lines and planes), we specifically refer to standard position vectors (that have tails at origin) and use heads of vectors as the required points.
In linear algebra (at least in a first course), we have a restricted scope for vectors. Vectors here mean the head end points of the standard position vectors (that have tails at origin). We are merely interested in points here. We refer to points (n-tuples or column matrices) as vectors.
In linear algebra, we do algebra such as addition and scalar multiplication on points to generate other points. We visualize the algebra on points by using directed line segments and using geometric constructions such as parallelogram diagonals for addition and scaling for scalar multiplication. The similarity of such geometric constructions with those of vectors in the general sense may make us think we are dealing with vectors in general sense. That is not so.
For example, consider u+ tv, where u,v are two constant vectors and t is a scalar parameter. Here, we visualize what is happening by using directed line segments for u and v and doing parallelogram diagonal constructions for addition. But, we should not confuse that the directed line segments forming the parallelogram diagonals as constituting the final resultant object. What really constitute the final resultant object are the head end points of the parallelogram diagonal directed line segments. Those end points happen to form a straight line in the case of u+tv.
Thus, the directed line segments are merely being used for geometric visualization of the algebra on points. Once we find the resultant points, the directed line segments (or their direction or magnitude) used in the process are discarded.
Why emphasize this so much when we do similar construction (and discard the diagonal line segments) while understanding vector equations in Precalculus? This is because in Precalculus treatment there is no confusion as to when we are dealing with directed line segments (signifying only direction and magnitude, and not the position) and when we are dealing with points(positions). In Precalculus, we use the terminology standard position vectors when we are dealing with points, and we use terminology vectors when we are interested just in direction and magnitude and not in the position. In linear algebra, we blatantly use the terminology vectors for points.
In computer graphics (https://ed.iitm.ac.in/~raman/Points-and-Vectors.pdf), we clearly make a distinction between points (position) and vectors(displacement).