There are minor variations in a few of the 630 boards, but notably the CPU is socketed, so it's not a huge stretch to note that a "Quadra" and an "LC" shared a platform. Granted, I still think talking about it as though it is a "real Quadra" is a huge stretch, primarily due to it sharing more similarities with the LC/II/III than most Quadras. It's all
badge engineering anyway.
The Quadra 605 is also "basically an LC" but perhaps the important lesson here is that Apple would basically have put any label on anything it thought would sell to a particular market. The Quadra 605 and 610 also shipped with LC040 chips, so saying "Quadra means full 040" is not accurate.
The labels, in general, were meant to be:
Performa: home computers
LC: school computers
Centris: office computers
Quadra: workstation-aspirational high end computers, "pro" computers.
Of these, it probably makes sense to list LC and Quadra first since Performa and Centris are both basically branding on the product to make a product sellable or attractive to a certain market.
The II naming kind of makes more sense in that realistically the main difference between most of Apple's hardware, especially out by 1993 or so, is expansion and exactly how cutting edge something is. Like I said, the LCIII or 475/605 isn't fundamentally incapable of anything you might have bought an 840 to do, but the 840 would do it faster and expansion capability is often a quality of life improvement, esp for people who want, say, multiple displays.
Apple should have called the SE/30 Macintosh IIae.
Apple's product stack was a huge burgeoning mess from around 1989 to 1997. You can look at any year and have to sit there and wonder why, say, both x and y exist, or why either exists when q exists, or why h was introduced as a replacement when a cost-reduced g that it replaced would have better served the market. (Interesting case in point: Once Performa and LC branding was gone, the Power Macintosh 6500 was still explicitly sold into edu, soho, and home markets. I think the only thing preventing it from being marketed as a corporate office desktop was that the 4400 and 7000 series existed.)
This kind of splitting still exists in the PC industry, although Intel takes care to put a little more differentiation into the processors, and Macs have Xeons now, which often have unique features (today: AVX-512, for example) that can get used by pro apps, making the rift a little wider between an iMac and an iMac Pro than a Centris and a Quadra was back in the day. Even a Centris 610 and a Quadra 950.
I think that badge engineering like that (or, in the PC market, selling particular chips and chipsets in systems designed certain ways) makes sense if your market is really huge and there truly are diverse needs, but I think Apple pretty handily over-estimated exactly how diverse the needs of most Mac users were at the time. (Very the opposite problem they've had in the past few years.)