The way I see it is that templates and inheritance are literally orthogonal concepts: Inheritance is “vertical” and goes down, from the abstract to the more and more concrete. A shape, a triange, an equilateral triangle.
Templates on the other hand are “horizontal” and define parallel instances of code that knowns nothing of each other. Sorting integers is formally the same as sorting doubles and sorting strings, but those are three entirely different functions. They all “look” the same from afar, but they have nothing to do with each other.
Inheritance provides runtime abstraction. Templates are code generation tools.
Because the concepts are orthogonal, they may happily be used together to work towards a common goal. My favourite example of this is type erasure, in which the type-erasing container contains a virtual base pointer to an implementation class, but there are arbitrarily many concrete implementations that are generated by a template derived class. Template code generation serves to fill an inheritance hierarchy. Magic.