Raids are multi-boss gauntlets (for example the Vaults of Xyren) with big reward tables: guaranteed loot plus a chance at rare uniques. Bosses are tougher single monsters with their own drop tables and kill counts. Boss and raid uniques are granted by the server when you complete the kill, and every kill is recorded — check the Collection Log and Leaderboard. You can spend credits to skip to a boss kill or pay a raid's skip cost.
A boss hunts you across its whole lair, further than any other monster will follow, and any minions it has summoned stay on the field with it. The way out of a boss fight is the way you came in.