Quite interesting your note, Sylvie. If having the jitters has come to mean being afraid, it is because someone who is in a panic usually acts in a nervous way, with fast repetitive movements. According to my Webster, the first meaning of to jitter is to make continuous fast repetitive movements. To have the jitters is to be in a panic to the point of fidgeting but a hyperkinetic boy may be fidgeting without having the jitters from being scared. I think we have to make out to jitter from to fidget. Thank you for pointing that out.
Taken from a dictinary published 1958: 'jitter' v.i. Colloq. to talk or act nervously [variant of 'chitter'] 'chitter' Scot. to shiver, as with cold [var of 'chatter'] (as in when your teeth are chattering).
To have the jitters denotes fear, yes, but mostly in the sense of some nervousness or anxiety being the cause, not fear in the sense of fright or terror.