From https://www.theguardian.com/us-news/article/2024/aug/04/jackson-mississippi-violent-crime-murder-capitol-police-tate-reeves:

“Historically, there is a difference between ‘sofa’ and ‘couch,’ and the origin of each term varies.” Feisal differentiates between the two for design purposes, even though many of her clients use them interchangeably.
When it comes to the term “sofa,” Feisal believes it carries a more design-oriented feel and an air of refinement. “I feel like it is the most-used term across the design industry,” she says. The designer tends to consider a couch as a more casual furnishing. “When I hear the word ‘couch,’ I think of something oversized, stuffed, and informal.”

From https://www.woodstockoutlet.com/blog/difference-between-sofas-and-couches:

The term “sofa” is a Turkish transliteration of the Arabic noun “suffah”, which is a bench or raised platform meant for sitting or reclining. Traditionally, a suffah would be draped in fabric and adorned with cushions.
True to its origin as a bench-like piece of furniture, sofas have well-defined arms and back. In addition, sofas are usually upholstered. While you can certainly recline on a sofa, they are primarily meant for sitting. As such, sofas tend to be more formal and are perfect for the living room.
To be honest, there aren’t too many differences between sofas and couches; the biggest difference is their intended use. The term “couch” is a derivative of the French verb “coucher”, which means to go to bed or lay down. Based on this early definition, couches are clearly meant for lounging about. In other words, sofas are meant for sitting while couches are equally meant for lying down.
Lastly, while a couch may indeed have a defined back and two armrests like a sofa, it doesn’t always. A couch may have only one arm, or none at all! Given this fact, couches have a less formal appearance and are most at home in the den, bonus room, media room, or “man-cave”.