Presets in Lr are just a group of parameters (like x amount of exposure, y amount of sharpening, etc) that are stored and can be applied. They can also include profiles.
Profiles are more fundamental in Lr. They apply during the RAW rendition. The Adobe Standard, eg, attempts to set a neutral rendition among many different cameras in order that they look as alike as possible. They also emulate camera-specific profiles, like the "Vivid" or "Portrait" you might have in your camera body to render JPEGs with a certain look. As with Capture One, Apple, Skylum, Affinity or any other developer they are essentially reverse engineering what the camera manufacturer does to get those looks. I don't see many high schooler interns making raw converters, but maybe someone here has worked at Adobe, Apple or Affinity and has inside info on how raw converters are developed. Maybe that explains why they take so long to appear in C1, Lr, etc
And of course profiles have always been important to those who use Lr and want accurate color; Colorchecker Passport users have been using that color card and the software to produce dcp files to insure correct color in any particular shoot for a long time. I guess they are mere "digital filters" but if you want accurate color then such a profile is rather essential.
Profiles have also been created by developers outside Adobe, commonly for film emulation. They usually sell those as presets, but those presets include profiles, which are more difficult to create. But presets were an easier way to deploy them. VSCO for example. The profiles within say their Olympus Film Kodak Gold preset is specific to that camera.
At the core of many of them are LUTs. These are used extensively in color grading for video work for many reasons. Often to give a certain cinematic look, but also to make sure different scenes shot at different times have a uniform and unjarring appearance. The LUTs can be created in say Photoshop or Affinity Pro, and applied in layers, which can also be blended. Then exported and turned into profiles, which if one wanted to, could be part of a preset. And sure, any dope with Photoshop can make a LUT. Making one that satisfies your DP or helps win you an Oscar is of course different, just as it's true that any high schooler with a Nikon can churn out photos, but may not be getting much gallery space.
The big deal about the profiles
for Lr is that they are more convenient to use now, and they make the use of LUTs easier as well since now a developer can either produce them or any one who can use Ps or Affinity. Photoshop users, of course, have been using them for a while, ditto for Premiere Pro, etc. (can't remember about C1 since I stopped using it a while ago). Most photographers who want the utmost in control of course use Ps over Lr since it has so many more tools for adjustments. But it's far easier to do batch work in Lr, or to browse through different treatments for multiple photos quickly, which is why, as already noted, Lr users have wanted this feature.
So if you are satisfied with your control over color and LUTs in your existing software, good for you. It's one of the reasons I thought Luminar had some advantages for some people (
Where to Get More LUTs | Skylum Blog (ex-Macphun)), as well as other programs (and BTW, if you can export a LUT as a .cube file from say Affinity or other program you use, you can use it to make a profile in Lr).