I'll try to answer in the parent commenter's place.
Prior generations of consoles were true-blue, capital-E "embedded". Whatever CPU they could get, graphics hardware that was custom built for that particular machine, and all sorts of weird coprocessors and quirks. For example, in the last generation, we had...
- The PlayStation 2, sporting a CPU with an almost[0] MIPS-compatible core with "vertex units", one of which is exposed to software as a custom MIPS coprocessor, a completely custom GPU architecture, a separate I/O processor that's also a PS1, custom sound mixing hardware, etc.
- The GameCube, sporting a PPC 750 with custom cache management and vector instructions[1], which you might know as the PowerPC G3 that you had in your iMac. The GPU is "ATI technology", but that's because ATI bought out the other company Nintendo contracted to make it, ArtX. And it also has custom audio hardware that runs on another chip with it's own memory.
- The Xbox, sporting... an Intel Celeron and an Nvidia GPU. Oh, wait, that's "just a PC".
Original Xbox is actually a good way to draw some red lines here, because while it is in some respects "just a PC", it's built a lot more like consoles are. All games run in Ring 0, and are very tightly coupled to the individual quirks of the system software. The "Nvidia GPU" is an NV2A, a custom design that Nvidia built specifically for the Xbox. Which itself has custom audio mixing and security hardware you would never find in a PC.
In contrast, while Xbox 360 and PS3 both were stuck with PPC[2], they also both had real operating system software that commercial games were expected to coexist with. On Xbox 360, there's a hypervisor that enforces strict code signing; on PS3 games additionally run in user mode. The existence of these OSes meant that system software could be updated in nontrivial ways, and the system software could do some amount of multitasking, like playing music alongside a game without degrading performance or crashing it. Y'know, like you can on a PC.
Contrast this again to the Nintendo Wii, which stuck with the PPC 750 and ArtX GPU, adding on a security processor designed by BroadOn[3] to do very rudimentary DRM. About the only thing Nintendo could sanely update without bricking systems was the Wii Menu, which is why we were able to get the little clock at the bottom of the screen. They couldn't, say, run disc games off the SD card or update the HOME Menu to have a music player or friends list or whatever, because the former runs in a security processor that exposes the SD card as a block device and the latter is a library Nintendo embedded into every game binary rather than a separate process with dedicated CPU time budgets.
And then the generation after that, Xbox One and PS4 both moved to AMD semicustom designs that had x86 CPUs and Radeon GPUs behind familiar APIs. They're so PC like that the first thing demoed on a hacked PS4 was running Steam and Portal. The Wii U was still kind of "console-like", but even that had an OS running on the actual application processor (albeit one of those weird designs with fixed process partitions like something written for a mainframe). And that got replaced with the Switch which has a proper microkernel operating system running on an Nvidia Tegra SoC that might have even wound up in an Android phone at some point!
Ok, that's "phone-like", not "PC-like", but the differences in systems design philosophy between the two is far smaller than the huge gulf between either of those and oldschool console / embedded systems.
[0] PS2 floating-point is NOWHERE NEAR IEEE standard, and games targeting PS2 tended to have lots of fun physics bugs on other hardware. Case in point: the Dolphin wiki article for True Crime: New York City, which is just a list of bugs the emulator isn't causing. https://wiki.dolphin-emu.org/index.php?title=True_Crime:_New...
[1] PPC 750 doesn't have vector normally; IBM added a set of "paired single" instructions that let it do math on 32-bit floats stored in a 64-bit float register.
[2] Right after Apple ditched it for power reasons, which totally would not blow up in Microsoft's face
[3] Which coincidentally was founded by the same ex-SGI guy (Wei Yen) who founded ArtX, and ran DRM software ported from another Wei Yen founded company - iQue.