A chain (alternatively string) is a group of stones that are all connected along the lines of the board. A single stone isolated from others of the same colour is a chain, in this sense.
For more formal talk, one can say:
A chain consists of
one stone together with all stones strictly connected to that stone (and only those).
That is, a chain is a collection of stones hanging together because of direct connection along a path made up of board lines.
Such a collection is often called a group, somewhat loosely. But groups in go are often made up of several chains that co-operate, without the solid connections that would link them into a single chain.
In various places, these have also been called 'armies' and 'units'.
The Japanese make no difference between stone and chain. Both are called ishi.