No, a 77mm filter does not screw directly onto an 82mm lens. The numbers refer to the diameter of the lens filter thread. The threads have to match unless you use an adapter ring.

Using a larger filter on a smaller lens

A step-up ring lets you put a larger filter on a lens with a smaller thread. For example, a 77-to-82mm step-up ring lets an 82mm filter mount on a 77mm lens.

This is a common way to standardize a collection around one larger filter size.

Using a smaller filter on a larger lens

A step-down ring lets a smaller filter attach to a larger lens thread, but it can physically block part of the image, especially on wide-angle lenses. That can cause dark corners or severe vignetting.

For that reason, photographers usually prefer stepping up rather than stepping down.

What the Ø symbol means

If a lens barrel says Ø77, it takes 77mm screw-in filters. If it says Ø82, it takes 82mm filters.

A real Canon example

The original Canon RF 70-200mm f/2.8L IS USM uses 77mm filters. The newer RF 70-200mm f/2.8L IS USM Z uses 82mm filters. Their names are very similar, but their filter sizes are not.

See the original RF 70-200mm f/2.8L reference.

One more catch: lens hoods

A step-up ring can interfere with the original lens hood because the larger filter extends beyond the normal filter diameter. If you rely on the hood, check physical clearance before standardizing on larger filters.