What the computer does is move electric charges around, change
magnetic state in some supports, read magnetic states, change some of
this into light pulses for transmission, and many others similar
Now it is up to you to interpret all that in whatever way you find
convenient, and give it a name accordingly.
Ignoring the physics, and going up one level, you manipulate bits. A
bit is just something that can have one of two possible states. All
that matters is that you can distinguish them. You may call them 0 and
1, or true and false, or Yin and Yan, or black and red, or up and
Then there ways of manipulating them that encode more complex things.
You can interpret a sequence of bits as a number, or as a letter, or
as a fragment of a text, or as a painting, or as a symphony. Your
choice, with appropriate encoding.
Then are you doing Arithmetic calculations, or composing music,
orwriting/reading a novel, or solving an equation ...? It depends on
the encoding and the manipulation.
But it is always calculation, in a sense, Calculation comes from the
latin calculus : stone, as stones were initially used for counting
(which is indeed arithmetic). But what survived is the idea of
manipulating stones. And the name calculus is generally used to
indicate some form of manipulation of entities supposed to represent something, usually the manipulation of symbol
in the modern world.
So, yes, the computer does calculations. But that only means it is
pushing bits around. And it may be for any purpose, since it is a
universal way of representing information.
Note: The use of the word calculus alone to mean also diffential and
integral calculus is more a linguistic accident. See:
What are the justifications and historical reasons regarding the choice between the words 'calculus' and 'algebra'?