I feel like people keep hanging up on home/handheld like it's some kind of dichotomy. Things don't have to be just one or the other, multifunction devices exist, and all devices exist on a sliding scale. The earliest "portable computers" were "portable" because they weren't hard-mounted to the floor and didn't require a crane or forklift to move.
The Switch, fundamentally, is a console. An electronic device dedicated to gaming. It's self-contained, with its own screen and battery, and small enough to comfortably move around, so it's fair to classify it as "portable". It also has extra power and functionality, including TV output, when plugged into its dedicated dock - thus allowing it to be classified as a "home console". But it's also portable, and its controllers can be attached to its body and allow it to be held while playing - making it also, potentially, a "handheld".
Neither its "home" nor its "handheld" state are absolute. At its core, the Switch is a portable console - with handheld and home console functionality options. Therefore, it's a portable handheld/home console hybrid, if you want to use a single long term.
In comparison, the Switch Lite is a handheld console - its 'handheld' form is permanent. It also, however, has portable console options, with allowing external controllers. It is not, even in options, a home console. So, it's a handheld portable console.
They both use the same hardware internally, have no software incompatibilities between them, can play the same games, and share enough features that while they're not the same, obviously, they are near enough in practice that they form the same platform, and can be combined together without unfairly misrepresenting either individual device's success.