There may be a difference between the usages of the words 'derivation' and 'inference' in English. I'll let native speakers make those distinctions. From a purely logical perspective, it all depends on how you want to define those terms. Here's one possibility.

You may, for instance, let derivations be sequences of sentences of a language system, each of which is either a primitive sentence of the system or follows from at least one of the sentences appearing before it in the derivation (this is what Carnap does). You may want to then confine the word 'inference' to particular individual steps in a derivation.

Example. If we let A, B, and C range over the sentences of our language system, "A, B, C" may be understood to be a derivation of C from A and B. Suppose A is of the form (if B then C), then C can be said to have been reached by the inference rule modus ponens. In more complicated examples, there will be lots of inferences, but still only a single derivation. So there seems to be a quantitative difference between 'derivation' and 'inference': a derivation consists of one or more inferences.