I realize this thread is old and marked as solved, but it should be noted that the original question does point out two completely separate workflows with different tool inputs.
Workflow one is Create Signatures and then run Maximum Likelihood Classification.
Workflow two is Train Maximum Likelihood Classification and then Classify Raster.
Workflow two is the basic classification which gives the user little control over the output, while workflow one allows the user to set a reject fraction and account for a priori knowledge. Workflow one also allows the user to output a confidence raster.
As is noted in the approved solution, the classification method is identical, it is only the output which is different.