Questions about state machines with a single stack for memory. They characterize the class of context-free languages.
The best category tag to use with this one is usually automata.
Except when conversion from or to automata is concerned, do not use when the question is about formal-grammars or properties of context-free formal-languages that do not relate to automata!
If you are unsure whether your question is about pushdown automata, you may want to check other questions or the Wikipedia page.
Do not use this tag for automata with more than one stack; tag those automata and computation-models.