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"Pop", "Hard, "Soft" are all words used to describe psychological /emotional reactions to contrast created by lighting gradients.
If you want to become proficient with lighting you need to get beyond the catchphrases and a understand the cause and effect of light, the surfaces it hits, the patterns it creates and how the brain reacts to them.
Start with understanding why we think we see 3D in a photo and what "normal" looks like. The baseline of "normal" is how we see objects modeled by light in nature. That varies with the angle sun. Here's my homage to the 2009 Winter solstice at high noon...
Knowing where the sun at noon would be in the sky from observation I aligned my creation facing south and tilted up the the sky so it would be lit with a "butterfly" pattern. The lighting at 10 AM and 2PM came more from the side and a lower 45° vertical angle.
What winds up happening on faces in natural light is that its dominant downward "key" light component puts highlights the upper surfaces of 3D objects. At 10AM in sunlight a ball facing south with the sun at 45° to right and 45° vertically would look like this:
You've seen an touched objects like that in person so upon seeing those illustrations your brain matches the contrast pattern — where the highlights and shadows are placed — and interprets the highlighted objects as being raised and the shaded areas lower based on those memories.
Now consider this image....
Flipping the image 180° changes the direction of the lighting and the 3D shape clues. You brain still recognizes the shape is a sphere from the pattern of highlights / shadows, but it doesn't seem as natural. Why? The light isn't coming from the more natural downward direction. That doesn't make it bad lighting or good lighting, just unnatural because it doesn't match what you see in nature or indoor lighting based on its direction most of the time.
As a photographer you can control how people will react to faces and objects by varying the key light angle. If as with the snow heads you keep it about 45° above the eye line and either centered on the nose, or 45° to the side of the nose the face will wind up modeled in a way it's 3D shape will be recognized immediately as the brain as being "normal".
That's what is happening in the example you posted. Look at the catchlights in the eyes at 10 o'clock. That's an indication the key light was 45° to the side and 45° higher than the point between the eyes — a classic textbook "short" lighting pattern. Why did that pattern, and butterfly become classic textbook patterns? Because our brains, seeing those patterns associate them with the natural 3D shape of human faces.
Key light position controls modeling, the illusion of 3D shape via highlight placement. Fill intensity and placement control shadow tone and than in turn influences how we interpret the environment the face or object is in and the time of day. For example compare the original with the same photo with lighter shadow on the subject...
Seeing the two side by side which appears more "normal"? Both. The one on the left is closer to how you'd normally see him during the day, the one on the left how you'd see him at night under a street light. Same lighting pattern but the difference in fill and shadow tone changes the emotional reaction. The darker shadows and lack of detail in the original evoke a more sinister reaction that the more normal lighting ratio on the left.
Now look and react to these examples....
The biggest difference between them is the specularity in the highlights. That's mostly a function of the skin texture. Oily skin, either naturally or due to make-up or lotions, will create a mirror-like (i.e. specular) reflection off the high points of the face similar to the sharply defined catchlights in the eyes. Specular reflections are mirror image of the light source.
In the boy / girl comparison I used my small speedlight diffuser for the boy then switched to my larger studio SB for the girl. The shadow clues on her face are lighter in tone than the boys, but the highlights are more specular. He washed his face before the photo, she wearing make-up didn't. The lighting in her shot could be said to "pop" more because there is more contrast in the highlights, but that's not particularly flattering on a conventional portrait like that.
The second was a "production" line head shot, one of 300 or so I took for a church directory by grabbing people as they arrived and shooting a single shot with my pair of speed lights. I spotted the glare on the skin — likely due to skin lotion — but couldn't prevent it when shooting. So in PP toned down the "hot" spots with cloning in darken mode. With both the girl and the woman the glare was the result of things they put on their skin not the skin itself. Normal skin doesn't cause specular hot spots, which is why hot spots in conventional portraits don't seem "normal". To the degree the lighting seems harsher on the darker skin its because the dark skin makes the highlights contrast more than on lighter tone skin. So more contrast is normal on darker complexions, but when the highlights get too specular the angle and pattern is normal but the glare isn't flattering. The clues are natural but the character of the source / skin combination isn't how we normally expect to see skin of any color. The solution to that problem? As the first boy / girl example shows increasing modifier size doesn't always work. The better solution is a freshly washed oil free face.
The take-away here is that everything we see in a photo gets compared to some mental impression of "normal". A photo taken with built in camera flash doesn't look normal. Why? Because the small source level with the lens causes the light to hit an unnaturally low angle creating small hot spots in the "wrong" places on the face, lower than seen in natural light. There are also no natural 45° downward shadow clues. The contrast pattern created by the light doesn't match the normal baseline for natural light we see faces in most of the time. Our reaction? "Gee that looks fake...." But take that same light source and move it 45° above the eye line and it will look more natural even when there are specular refections. Why? The specular reflections while harsh are in the same places they would be in natural lighting at a downward 45° angle.