I have seen two slightly different characterizations of the weak compactness property, pertaining to weakly compact cardinals.
Any $\kappa$-satisfiable set $\Sigma$ of $L_{\kappa,\kappa}$-sentences with $|\Sigma|\le \kappa$ is satisfiable.
Any $\kappa$-satisfiable set $\Sigma$ of $L_{\kappa,\kappa}$-sentences in which no more than $\kappa$ non-logical symbols occur is satisfiable.
It's clear that the second statement implies the first, and seems at first pass to be stronger. For instance, it's not obvious to me how to prove $\kappa$ is a strong limit from the first statement, though it's easy to show it is a regular limit. I've seen sources that use the first formulation (e.g. Jech) make the additional stipulation that $\kappa$ is inaccessible, but others (e.g. Drake) don't.
Is the first statement strictly weaker than the second or is it equivalent, and is there an easy way to see why?
EDIT Looking more closely at Drake, he assumes $\kappa$ is inaccessible when he shows all the standard equivalences, so this seems to suggest the additional assumption is required, whereas the second formulation implies inaccessibility. Other sources have corroborated. Still, I'd be interested if there is a nice example of a non-strong-limit that is weakly compact in the first sense, or a nice alternative characterization of cardinals of this sort.