Spectre breaks the isolation between different applications. It allows an attacker to trick error-free programs, which follow best practices, into leaking their secrets
CVE-2017-5753 and CVE-2017-5715 are the official references to Spectre maintained by MITRE.
Meltdown breaks the most fundamental isolation between user applications and the operating system. This attack allows a program to access the memory, and thus also the secrets, of other programs and the operating system.
CVE-2017-5754 is the official reference to Meltdown maintained by MITRE.