There is the Mealy machine, where the outputs depend on the state and the inputs.
There is the Moore machine, where the outpust depend only on the state.
A state table is used for a Moore machine and it shows the 'next' state for every combination of 'inputs' and 'present' state.
A transition table is used for a Mealy machine to show the 'next' state and the 'outputs' for every combination of 'inputs' and 'present' state.