Perhaps you mean the difference between a copula and a non-copular verb?
The main difference is that while the copula is used as a linking verb, which
defines the subject, a non-copular verb defines the action.
- John is a doctor. (copula)
- John ate an apple. (action)
This is a rather clear concept for someone who studies Languages or Linguistics, but I understand it might be harder for someone who is not so into this subject, so I'll try to explain more in depth what it means to define the subject or the action.
Let me make an example in Italian: "Giovanni è felice." It means "John is happy".
The verb "è" in this sentence is not about something that Giovanni is doing, but "è felice" altogether is defining what Giovanni is (in general or in that particular moment, not really important). Note that "è felice" in the analysis is considered as one thing. In Italian it's called "predicato nominale", I'm not sure about the English name.
Defining the subject
Copular verbs don't express actions, like I said. When you state that "someone is something", that someone is not doing anything. There is no action being "made". Rather there is a feature being assigned to a subject.
Taking the example above, when we say that "John is a doctor", John is not **doctoring*. "Doctor" is what John is, not what John is doing.
Defining the action
Instead, when we say that "John ate an apple", we do have an action being defined. "Apple" is not what John is, but rather "what" is sustaining the action that is being performed by John.
On a final note, not only the verb to be can be a copula. Also verbs like to seem, or to appear can be copulae (they can be, i.e. they can be non-copular too). Check this list on Wikipedia about English copulae.
Since you mentioned "Transitivity", a transitive verb is a verb where the action is being performed by the subject and that is being sustained by an object. Read more about it on the wikipedia page for Transitivity, but to explain it here:
- The dog barks. (intransitive)
- John likes apples. (transitive)
Transitivity is closely related to Valency which is about the possibility for some verbs to sustain other arguments other than the Direct Object, as in "John gave Mary a pen". You can see the link above or this answer I wrote on EL&U.