Inheritance is nothing more or less than composition + implementing the same interface + saving a bit of boilerplate.

When class A inherits from class B, that is equivalent to class A containing an object of class B, and recoding the same interface as class B, and automatically generating method stubs for every method of the interface that call that same method on your B.

That is, these two are perfectly equivalent:

  class B {
    public void foo() {
    } 
  } 

  class A_inheritance extends B {
  }

  class A_composition implements B {
    private B super;

    public void foo() {
      super.foo();
  }

This is pseudo-code because Java distinguishes between Interfaces and Classes, and doesn't have a way to refer to the Interface of a Class. In C++, which doesn't make this distinction, it's even more equivalent. Especially since C++ allows multiple inheritance, so it can even model a class composing multiple objects.

The problem with inheritance is that people get taught to use it for modeling purposes, instead of using it for what it actually does - when you need polymorphism with virtual dispatch, which isn't all that common in practice. That is, inheritance should only be used if you need to have somewhere in you code base a collection of different objects that get called in the same way but have to execute different code, and you can only find out at runtime which is which.

For your students and employees and users example, the only reason to make Student and Employee inherit from User would be if there is a reason to have a collection of Users that you need to interact with, and you expect that different things will happen if a User is an Employee than if that User is a Student. This also implies that a Student can't be an Employee and vice versa (but you could have a third type, StudentEmployee, which may need to do something different from either a Student or an Employee). This is pretty unlikely for this scenario, so inheritance is unlikely to be a good idea.

Note also that deep class hierarchies are also extremely unlikely to be a good idea by this standard: if classes A and B derive from C, that doesn't mean class D can derive from A - that is only useful if you have a collection of As that can be either A or D, and you actually need them to do different things. If you simply need a third type of behavior for Cs, D should be a subclass of C instead.

I'd also note that my definition applies for inheritance in the general case - whether the parent is an interface-only class or a concrete class with fields and methods and everything. I don't thing the distinction between "interface inheritance" and "implementation inheritance" is meaningful.