The following is the definition of a cartesian closed category in Goldblatt's Topoi:
Definition 1: A category $C$ is cartesian closed if (1) it is finitely complete, i.e. every finite diagram has a limit, and (2) it has exponentials.
When I look at other sources (for example wikipedia, Awodey's Category Theory, Leinster's Basic Category Theory), the usual definition is as follows:
Definition 2: A category $C$ is cartesian closed if (1) it has finite products and (2) it has exponentials.
Now, clearly condition (2) in the two definitions are the same. However, it seems to me that condition (1) of the first definition is strictly stronger than definition (1) of the second definition, since finite products are a special case of a limit of a finite diagram. Is this correct, or are the two definitions equivalent? If they are not equivalent, then what could be the reason for Goldblatt's slightly different definition in the context of toposes?
Definition 1 really is a stronger requirement, than Definition 2. A justification can (apparently) be found in "Sketches of an elephant - A 1.5 Cartesian closed categories" (the part below Lemma 1.5.1).
I suppose Goldblatt decided to include finitely completeness in his definition because the only thing missing in Def. 2 is the existence of equalizers and because regular categories (every topos is a regular category) are usually assumed to have finite limits (e.g. the existence of pullbacks makes composition of internal relations possible).
However, Def. 2 is better established, so much that it is generalized by the notion of a "closed monoidal category", so I would encourage anyone to use this definition.