The basics: safe vs. vault.
A safe is a securely constructed box of a size which could be anything from that of a mailbox to a double refrigerator. Typical UL ratings for safes are TL-15, TL-30, TRTL-30, TL-15x6, and TRTL 30x6. Underwriters Laboratories rates burglary resistance of safes in terms of minutes, not hours.
A vault is a room of securely constructed walls, ceiling, and floor in combination with a burglary-rated door. The UL ratings for vaults and vault doors are (ascending order) Class M, Class I, Class 2 (II), and Class 3 (III). Be aware that there are vault-appearing doors with combination locks which are rated for fire protection, intended primarily for document storage.