the Pasteboard Area

ElementX,

In addition to what Monika and Brad said, the work area was once called the Artwork Board (which was later widened from 1296pt to 16384pt (a good 227 inches and a half (5/9) in accordance with its being based on points), and a shortened form of the name became Artboard with its current meaning.

Both work area and Artwork Board give a good impression corresponding to a drawing board (a desk or solid board that can be horizontal or set at an angle) of fixed size for work like drawing, sketching, writing, basically on paper.

All this is different to the work canvas/canvas/Canvas in Photoshop with its variable which gives a good impression corresponding to a canvas (plain woven fabric) of a chosen size used as a support for a painting.

The work area has also come to be called the workspace to ensure confusion with the working spaces, once a term concerning colours (RGB and CMYK) also called colour spaces, and currently more woollily the work area and/or the auxiliary parts placed on it.

Among these parts are panels, which some of us are still inclined to call palettes.

The term for the part of the work area outside the Artboard was once called the scratch area.

Inevitably, one day someone (also) working with Photoshop started using the term Canvas, which has now taken over, as in Large Canvas.

So all sorts of terms may have come from actual sources such as The Fine Manual (in the old days) or made up on the go, and they may depend on age, disposition, moon, rifts and other irregularities in the space time, and more.

In other words, let nothing surprise you, least of all this bold Adobe Help page introductory statement:

"Artboards let you streamline the design process and work on designs on an infinite canvas."

https://helpx.adobe.com/illustrator/using/introduction-to-artboards.html

When Illustrator was first created in the 80s, it had a fixed artwork area, essentailly a large blank piece of paper to draw on (the "canvas"). Any graphic created was drawn on that work area and then exported as a file that would be just the size of that graphic (say, a logo) and nothing else. As Illustrator got better and more sophisticated, people started to need more specific layouts (like designing full pages) so the concept of Artboards was created to define, on that big canvas, a certain page size, plus you could add as many artboards of different sizes and shapes as you wanted, but this still occupied space on the overall canvas. You can see this area (which is normally* about 227inches x 227 inches) by zooming out as far as you can. e.g. here's a screen grab of a letter sized artboard in the center of the canvas limits, zoomed all the way out. "Pasteboard" is a term more connected to page layout programs like InDesign, which is the area outside your page where you can store objects graphics, etc., not used on your page, but over time, this term also came to be used to describe the open area around Artboards in Illustrator.

*I say normally since it's also possible to expand this work area in certain circumstances for extra large artwork, aka "large canvas")

Things are sometimes called differently by everyone. Usually the Pasteboard is the area outside of the artboards in your file. You can put elements there and they also are saved as long as you save an AI document. With other file formats it depends on the options.