'atom' is usually seen from list processing. In Common Lisp something is either a non-empty list or an atom. In former times an atom was also called 'atomic symbol', which is something slightly different. Now in Common Lisp atoms are not only symbols, but everything else which is not a cons cell (examples: strings, numbers, hashtables, streams, ...).
If something is not an atom (is a cons), the operations CAR, CDR, FIRST and REST can be used.
So atom is a group of data structure. A symbol is a certain data structure, which also happens to be an atom.