I've been told in the past that it is a specific effect, but I've forgotten the name. Does anyone know what the effect is called?
It's hard to tell what you're looking for based on a brief description and just two examples. Here's an image that was taken on a FujiFilm X-E2 at ISO 200, 1/350s, with an XC 50-230/4.5-6.7 OIS-II lens at 230mm F6.7. No special processing before uploading, though Imgur may do some processing that is out of my control.
If it illustrates what you are seeking, there are a number of options that may suit you. (Otherwise, I have no idea what you're asking. Clarification and more examples would be helpful.)
Select the subject. For instance, with food photography, a lot of time can be spent sorting ingredients, re-cooking dishes, and plating multiple variations.
Experiment with composition. Even just slightly shifting the subject, eg, the location of foods on a plate, can greatly improve a photograph.
Increase aperture, focal length, and subject-to-background distance to create a shallow depth of field that results in a sharp subject with blurred background. Sensor size is useless if these elements aren't in place.
Reduce captured noise by using low ISO or image averaging.
Change camera-specific settings. No choice but to read the manual.
Create motion blur by moving the camera with a subject or using long shutter speeds with moving water.
Photograph at macro-scale, which inherently has a shallow depth of field. Extension tubes are a good way to get started. Don't worry about the math. Just get a cheap set with pass-through electronics, and start experimenting.
Use studio lighting techniques to separate foreground and background.
Resize so that imperfections are shrunken down to sub-pixel sizes. This is somewhat related to pixel binning.
Reduce noise along with techniques to avoid destroying detail in the wrong places, such as creating masks based on high pass or edge detection filters. If done excessively, people can end up looking like wax figures.
Use magical plugins and filters, which include a "liquify" plugin (iWarp on GIMP) that performs digital cosmetic surgery. This seems like what you may have been initially asking about, but I'm no good at casting such spells.
Keeping this simple: In Adobe Lightroom, the sliders for noise reduction give the smooth plasticy look. The luminance noise slider creates the effect far more than does the slider for damping chromatic noise. Warning: the smoothing effect can easily be overdone, so be judicious with it. It's most creepy when overdone on people; you can get away with a bit more on nonhuman natural subjects, and more still on manufactured things.
There are fancier techniques that create layers in Photoshop, which separate luminance variation, from chromatic variation. You then blur the chroma layer(s) sufficient to achieve the smooth skin tone you want, while retaining all of the skin's the textural clarity in the luma layer. There are how-to's out there (Google them). I don't use them enough to write a good walk through, but others have made great how-to's. Unlike the noise sliders in Lightroom, this effect creates some extremely high-end images, used in ads to sell make-up and anything in the fashion world. They can give the subject the skin tone of a 10-year-old, while retaining all the texture that makes the photo look real. In comparison, the plasticy look from luma noise smoothing always looks unnatural.
From the images you posted, it seems like the look you want is going to come from a very sharp, fast lens used with what looks like at least a two— maybe several—flash system. Controlled studio light like that is going to get you 90% of the way there— the rest can be done in post as has been described.