Due to the ambiguity of the question, there are many possible words that can be used to describe the "ends" of a blood vessel. The most important part, as others have mentioned, is providing a reference point.
Superficial and deep refer to the location relative to the skin but a vein can traverse the anterior and posterior parts of an appendage.
Distal and proximal generally refer to distance from an attachment or point. For example, a ventriculoperitoneal (VP) shunt is used to relieve pressure that builds within the brain. This shunt originates in a ventricle in the brain and empties in the peritoneal cavity. Thus, the proximal end of the shunt is in the brain and the distal end is located within the peritoneal cavity.
Next is inferior and superior which are used to reference above and below a certain point. An example are the venae cavae. The inferior vena cava returns blood to the right atrium from the lower body while the superior vena cava returns blood to the right atrium from the upper portion of the body.
A last point of clarification: arteries and veins are classified by function. Thus, arteries carry blood away from the heart and veins carry blood to the heart.