Encapsulation hides variables or some implementation that may be changed so often in a class to prevent outsiders access it directly. They must access it via getter and setter methods.

Abstraction is used to hide something too, but in a higher degree (class, interface). Clients who use an abstract class (or interface) do not care about what it was, they just need to know what it can do.

Most answers here focus on OOP but encapsulation begins much earlier:

• Every function is an encapsulation; in pseudocode:

  point x = { 1, 4 }
  point y = { 23, 42 }
  
  numeric d = distance(x, y)
  

  Here, distance encapsulates the calculation of the (Euclidean) distance between two points in a plane: it hides implementation details. This is encapsulation, pure and simple.

• Abstraction is the process of generalisation: taking a concrete implementation and making it applicable to different, albeit somewhat related, types of data. The classical example of abstraction is C’s qsort function to sort data:

  The thing about qsort is that it doesn't care about the data it sorts — in fact, it doesn’t know what data it sorts. Rather, its input type is a typeless pointer (void*) which is just C’s way of saying “I don't care about the type of data” (this is also called type erasure). The important point is that the implementation of qsort always stays the same, regardless of data type. The only thing that has to change is the compare function, which differs from data type to data type. qsort therefore expects the user to provide said compare function as a function argument.

Encapsulation and abstraction go hand in hand so much so that you could make the point that they are truly inseparable. For practical purposes, this is probably true; that said, here’s an encapsulation that’s not much of an abstraction:

class point {
    numeric x
    numeric y
}

We encapsulate the point’s coordinate, but we don’t materially abstract them away, beyond grouping them logically.

And here’s an example of abstraction that’s not encapsulation:

T pi<T> = 3.1415926535

This is a generic variable pi with a given value (π), and the declaration doesn’t care about the exact type of the variable. Admittedly, I’d be hard-pressed to find something like this in real code: abstraction virtually always uses encapsulation. However, the above does actually exist in C++(14), via variable templates (= generic templates for variables); with a slightly more complex syntax, e.g.:

template <typename T> constexpr T pi = T{3.1415926535};

Abstraction is the concept of describing something in simpler terms, i.e abstracting away the details, in order to focus on what is important (This is also seen in abstract art, for example, where the artist focuses on the building blocks of images, such as colour or shapes). The same idea translates to OOP by using an inheritance hierarchy, where more abstract concepts are at the top and more concrete ideas, at the bottom, build upon their abstractions. At its most abstract level there is no implementation details at all and perhaps very few commonalities, which are added as the abstraction decreases.

As an example, at the top might be an interface with a single method, then the next level, provides several abstract classes, which may or may not fill in some of the details about the top level, but branches by adding their own abstract methods, then for each of these abstract classes are concrete classes providing implementations of all the remaining methods.

Encapsulation is a technique. It may or may not be for aiding in abstraction, but it is certainly about information hiding and/or organisation. It demands data and functions be grouped in some way - of course good OOP practice demands that they should be grouped by abstraction. However, there are other uses which just aid in maintainability etc.