Modern vs. contemporary art: what's the actual difference?
People use "modern" and "contemporary" as if they mean the same thing. They don't, and once you know the dividing line, half the confusion in any gallery disappears.

The one-sentence answer
Modern art is roughly 1860s–1970s. Contemporary art is roughly 1970–now. The split is about when the work was made, not what it looks like.
Modern art: the great experiments
"Modern" is a historical period that has ended. It runs from the Impressionists breaking with realism, through Cubism, Surrealism, Bauhaus and Abstract Expressionism. Its through-line was a series of bold experiments about what a picture could even be, a story we tell in why art movements still matter.
Contemporary art: the art of right now
Contemporary art is the art of our own moment, installation, video, performance, conceptual work, digital and beyond. It's less about a single style and more about ideas, identity and context. The materials are wide open; a contemporary piece might be a neon sign, a pile of sweets, or a coded animation.
Why the mix-up matters
Calling a brand-new painting "modern" is a bit like calling a 2024 phone "vintage tech", it quietly misplaces it in time. Getting the word right is the first step to reading what a work is actually trying to do.
Next, the question that trips up everyone: why is abstract art considered art at all? And for wandering wider into history and culture, more on art and culture is a good broad read.