Jisho

They have seperate origins. The N levels are assigned by the Jisho.org team, possibly extracted from a specific Database for that. The N levels generally refer to the Japanese language foundations proficiency levels which can be acquired through their tests (日本語能力試験). They are similar to e.g. the European A2 - C2 levels. But there currently exists no official dokument stating which words are belonging to which proficiency grade, thus all modern N classification is based on assumption and old material. This, as well as the below, are just rough estimates to guide the learner.

Afaik the common word classification comes from JMdictDB's priority tagging system, where the editors assign different priority tags based on inclusion in certain word popularity surveys. But it is a manual process and can often be a bit inaccurate. It is more of a rough estimate than a precise classification.

thanks, Sombrero

Also see the reply from Kim in this thread: https://jisho.org/forum/5ac1ef7c12a537285b0000a8-how-does-jisho-dot-com-decide-whether-a-word-is-a-common-word-or-not