An artist is someone that creates art in any form (sculpting, painting, jewelry making, etc) but an illustrator is primarily someone working on 2d via painting or linework. That's how I see it anyway. :)

In a simple way, all illustrators are artists, but not all artists are illustrators. Singers and musicians, for example, are artists too.

Contingency

Art is poetry and illustration is prose.

Artist: do what you want. Illustrator: do what they want.

an illustrator is an artist but not all artists are illustrators.

“Artist” is more of an umbrella term for various different things (it’s just someone who makes art), illustrators are just one type of artist (like animators, graphic designers, painters, etc)

Illustrators may stop creating visual art if the work dries up. Artists won’t.

Think of art as the main body that illustration falls under. Illustration is one of many art forms that aims to visually narrate an idea or story. It is however separate from graphic design (that focuses on layouts, logos and typography) and fine art (self expression, abstract art, etc). It is also separate from concept art. Illustrators ARE artists but not every artist is an illustrator.

An illustrator designs art to solve a problem, a need or tell a story. Artists express ideas and messages in a personal way, sometimes subjective, sometimes for others and this can take any form - painting, sculpture, music, spoken word etc. An illustrator actually illustrates a specific idea or message in a predetermined form - can include traditional 2d work, vector art, logo design, cover art, pattern design etc. Most illustrators are infact artists, but not all artists are illustrators.