Just as most agile projects aren't Agile, most waterfall projects weren't strict Waterfall as it was preached.

That being said, when for instance you had a project that should take 2 years and involve a dozen team, you'd try to cut it in 3 or 4 phases, to even if it would only be "released" and fully tested at the end of it all. At least if your goal was to have it see the light in a reasonable time frame.

Where I worked we also did integration runs at given checkpoints to be able to iron out issues earlier in the process.

PS: on agile, the main specificity I'm seeing is the ability to infinitely extend a project as the scope and specs are typically set on the go. Which is a feature if you're a contractor for a project. you can't do that with waterfall.

Most shops have a mix of pre-planning and on-the go specing to get a realistic process.