Conoscente means acquaintance, while amico means friend. As you surely now true friends are rare in life while acquaintances abound. Therefore I must agree with Andrew that the difference is big indeed!

Conoscente is: a) somebody whose existence you are aware of b) somebody that you will recognize when you meet him or her and say hello to. Amico is: a) he must obviously be a 'conoscente'. b) somebody whose company you enjoy. c) somebody that you will help if need arises, and this must be reciprocal. d) somebody you trust, and he trusts you == Just for completenes, and because I ebnjopy writing in English: Usually /conoscente/ and /amico/ is bidirectional (symmetric behaviour), while, for instance /being fond of somebody/ is usually not a symmetric behaviour. Wish you find good and sincere friends!

The difference is BIG, very BIG.