A large amount come from the campaign, some of which require you to play it more than once. There are 42 basic achievements, plus 5 from each DLC.
While Weapon, Kit, and Vehicle unlocks are their own reward, you also get Service Stars, and for either 5 medals or 500 kills with a weapon, you get a Mastery Dog Tag. Ribbons and Medals give you bonus XP when you earn them, and some are requirements for Assignments. The Awards are Ribbons (gained by doing something a number of times in a round), and Medals (awarded for every 50 Ribbons of a given type).
There are four regular assignments which give weapons - the Gold (Kit) Expert assignments. Most of the useful unlock items are obtained from the DLC assignments. Battlefield 4 has some assignments which offer weapons and equipment of use in the game, but most awards, assignments, and achievements give only cosmetic items, or fill a place on your wall of achievements. One of the challenges players give themselves is 100% completion of all unlocks and achievements in a game. Or how to get 100% completion in Battlefield 4.