Yes, you are correct - it is a "kind of military person".  It is a rank in the military - I think below a sergeant.   However, a second meaning is to do with the body or physical form - hence 'corporal' punishment, or bodily punishment.  Interestingly, there is a third meaning: it is the cloth which the 'plate' and 'chalice' are placed on during a Eucharist service in Christian churches!
And, yes, a synonym for 'corporal' is 'corporeal'.  You are correct.   :-)