Fide = pistis = faith
An interesting idea I came across recently concerns the Latin influence on the meaning of "faith" in the NT.
The Greek word for "faith"/"faithfulness" is pistis. The Latin word for it is fide. (Hence for example "sola fide" = salvation by "faith alone") Fide means "allegiance", and it was a very important word to the Romans at the time of Jesus. (It does not in any way, shape, or form ever mean "belief", as far as I know) Allegiance to the Emperor Caesar was the single most important political thing there was. The word was used to describe the Roman army's oath of allegiance, and even appeared on coins. "Allegiance to Caesar as Lord"... the political slogan of the Roman Empire. "Allegiance to Christ as Lord"... Paul's slogan to the Christians he was writing to.
Here's the thing: Paul is writing to major Roman cities. Their understanding and use of "pistis" will be being influenced by the Latin equivalent "fide", and similarly by the popular political phrases. Paul being widely travelled would have to know this. It is undeniable that when Paul uses the phrase of "faithful to Christ as Lord" he is deliberately paralleling the Roman political phrase of faithfulness to Caesar as Lord.
This, perhaps, helps solve an interesting problem. Namely why Paul seems to use pistis to mean "allegiance"/"faithfulness", while James uses it to mean "belief". Paul's usage of the word is being influenced by its Roman usage, while James is using it in a non-Romanised way. In other words, Paul is deliberately choosing language that he knows his audience will understand and making his message more interesting and relevant to his readers by explaining it in terms of the major issues of the day that were relevant to them.