You essentially got the concept right, concrete is essentially artificial stone that can be initially poured into a mould and once set has characteristics similar to some types of stone.
Concrete is a mix of elements with different sizes (granulometry), like sand, gravel, (crushed) rock (of various sizes), with one or more binding agents, it is a "conglomerate" (in quite a few languages concrete is properly called the equvalent "cement conglomerate", in English "conglomerate" designs a natural rock that shares the same kind of structure:
https://en.wikipedia.org/wiki/Conglomerate_(geology)
Cement is just the most used binding agent, usually very, very fine.
As a comparison, what is usually called asphalt is another kind of conglomerate where the binding agent is bitumen.
Cement by itself has very good hardness but it is fragile and/or brittle (and it has very relevant shrinking when setting).
Mortar is cement+sand, it is a sort of midway between the two.
Stone (it depends on which kind of stone we are talking) is ultimately a sort of natural concrete where the particles (that may also be monogranular) have been "assembled" by pressure (and heat) over countless time.
Typically stone is quarried from very huge monolithic deposits, or it comes in large slabs, that are cut to make (transportable) bricks or samller slabs, that you then assemble with mortar.
Chiseling is not involved in building with stone (anymore) if not for decoration/aesthetic reasons.
Whether casting concrete or assembling stone elements in - say - a wall is faster or slower it is hard to say, it greatly depends on the structure, on the available tools/equipment and local costs for the one or the other and for the labour, usually concrete is cheaper because the components cost less, the tools and equipments are readily available and there is less labor involved, but it depends on the specific place/country.
In the case of reinforced concrete, the advantage is that you can make much thinner structures with same or better structural strength than masonry.