Playing on a TV makes a world of difference for a lot of people, and being portable is a different experience as well. At least, that much was true in the past, pre-Switch.
The distinction probably is more notable if you grew up with handhelds during the 90s. There were considerable disparities between something like the Game Boy and NES/SNES at the time. Handhelds were typically and notably behind the more powerful home consoles. For most of us it was Game Boy or Game Gear, both or which lagged behind their home console counterparts. The Lynx, Turbo Express, and Nomad all pushed handhelds to rival home consoles, but they were expensive and no one I knew grew up with them around.
By the late 90s, you had full-blown 3D graphics on home consoles, while the GBC (then the only worthwhile handheld left standing) finally gave color to its 8-bit graphics. I mean, shortly after the GBC launched in Japan, the Dreamcast came out there a month later. So, this long period of time where handheld hardware was stuck at 16-bit graphics at best while home consoles went 32-bit and 3D (along with CD quality audio) heavily reinforced the idea that there were 2 tiers of consoles. It's a matter of console "power" which went on to affect what kinds of games could be offered on each platform, which in turn affects your experience as a gamer. I was a huge GB fan, so it was very clear to me that handhelds and home consoles were almost two different realms.
Fast forward to the next millennium, and you get the GBA, which was a massive leap for handhelds. The new Game Boy jumps several "generations" worth of tech to play catch-up. Where the GBC was stuck somewhere between an NES and SNES, the GBA goes well beyond the SNES (besides audio quality) to just about below the Saturn in terms of 2D capabilities. A few years later, and the NDS has absolutely the best native 2D hardware, and decent 3D support, and finally high-quality audio. The PSP comes along and it's basically a portable PS1.5. By the time the 3DS and Vita come out the "gap" between handheld and console feels minimal in terms of what types of games people can expect from each. And then the Switch destroys the line between these two categories.
So, I feel the later you start really getting into handhelds, the less of a difference you see. Even nowadays, kids with their phones and Android handhelds, or Shields might just shrug at the notion that handhelds and home consoles are different types of consoles. Post-2001, this is rapidly becoming less and less true, but historically speaking, I really think there was a solid "barrier" or something that defined handhelds and home consoles. So to answer the question "Why split consoles into these two groups?", I'd argue it's important if you want to accurately describe gaming history.
tl;dr - I am old, and I remember when handhelds very much lagged in many regards behind home consoles.
The distinction probably is more notable if you grew up with handhelds during the 90s. There were considerable disparities between something like the Game Boy and NES/SNES at the time. Handhelds were typically and notably behind the more powerful home consoles. For most of us it was Game Boy or Game Gear, both or which lagged behind their home console counterparts. The Lynx, Turbo Express, and Nomad all pushed handhelds to rival home consoles, but they were expensive and no one I knew grew up with them around.
By the late 90s, you had full-blown 3D graphics on home consoles, while the GBC (then the only worthwhile handheld left standing) finally gave color to its 8-bit graphics. I mean, shortly after the GBC launched in Japan, the Dreamcast came out there a month later. So, this long period of time where handheld hardware was stuck at 16-bit graphics at best while home consoles went 32-bit and 3D (along with CD quality audio) heavily reinforced the idea that there were 2 tiers of consoles. It's a matter of console "power" which went on to affect what kinds of games could be offered on each platform, which in turn affects your experience as a gamer. I was a huge GB fan, so it was very clear to me that handhelds and home consoles were almost two different realms.
Fast forward to the next millennium, and you get the GBA, which was a massive leap for handhelds. The new Game Boy jumps several "generations" worth of tech to play catch-up. Where the GBC was stuck somewhere between an NES and SNES, the GBA goes well beyond the SNES (besides audio quality) to just about below the Saturn in terms of 2D capabilities. A few years later, and the NDS has absolutely the best native 2D hardware, and decent 3D support, and finally high-quality audio. The PSP comes along and it's basically a portable PS1.5. By the time the 3DS and Vita come out the "gap" between handheld and console feels minimal in terms of what types of games people can expect from each. And then the Switch destroys the line between these two categories.
So, I feel the later you start really getting into handhelds, the less of a difference you see. Even nowadays, kids with their phones and Android handhelds, or Shields might just shrug at the notion that handhelds and home consoles are different types of consoles. Post-2001, this is rapidly becoming less and less true, but historically speaking, I really think there was a solid "barrier" or something that defined handhelds and home consoles. So to answer the question "Why split consoles into these two groups?", I'd argue it's important if you want to accurately describe gaming history.
tl;dr - I am old, and I remember when handhelds very much lagged in many regards behind home consoles.