There are two senses in which an automaton A is said to recognize (or accept) a language L: for any input string w,
(a) A halts and indicates that it accepts or rejects w, corresponding with whether or not w ∈ L;
(b) A halts if w ∈ L and fails to halt otherwise.
In the case of Turing machines, the languages recognizable in sense (a) and the weaker sense (b) are the recursive sets and the recursively enumerable sets, respectively.
Turing machines are a particular kind of automaton. Other kinds include the finite-state automaton, pushdown automaton, and linear-bounded automaton. Sequential machines are automata that produce an output string. According to the Church–Turing thesis, if a language is recognizable (in either of the above senses) by any kind of automaton, it is so recognizable by a Turing machine.
au·tom·a·ton / ôˈtämətən; -ˌtän/ • n. (pl. -ta / -tə/ or -tons ) a moving mechanical device made in imitation of a human being. ∎ a machine that performs a function according to a predetermined set of coded instructions, esp. one capable of a range of programmed responses to different circumstances. ∎ used in similes and comparisons to refer to a person who seems to act in a mechanical or unemotional way: she went about her preparations like an automaton.