They may achieve the same result, depending on what you need to do.

for example, for deadheading -- you can snip off with your fingers, cut with scissors, or maybe shear it with something that is not a scissor. In the end, you are "deadheading" the flower, regardless of which method you use. Some people like to use scissors or pruners because there is some level of argument about how much stress you should give your plants. Clean cuts won't pull on the stem as you try to remove the flower or leaf, etc.

As regarding to deadheading, it is usually only referring to the flower part, but you can take a few stems and leaves with it, which is up to you. However, I haven't read about deadheading by cutting the stem to the ground.

For many plants, even if they just have one flower along a stem, it is better to leave that stem to feed the plant. One example exception to this is for some roses and certain other flowers. If you cut back the flower and a bit of stem, you encourage new growth that should make an additional bunch of flowers later in the season.

In regard to your dianthus, sometimes the leaves and stems will dry up and die. It's always a good idea to remove dead growth, so the instructions you read about shearing seem to be referring to this.

Dianthus can also be deadheaded to help it flourish more but honestly, I find that the dianthus grows quite fast and well that I mostly leave it alone. Some will be flowering, some dying, and some making seeds -- but all of it looks just great or are desired by me (since I do wants seeds for some varieties)

I don't mess with my dianthus either. That's part of the point to me - it can do it's thing and I don't have to put any time or energy into upkeeping it.

When my dianthus finish I cut all the flower stems off down to the level of the foliage with grass shears. That way I have nice blue mounds in summer without stems sticking up which I do not care for. They bloom again in fall or will put out a few in summer if we get rain. I call that deadheading. I just did this last week, it took only a few minutes. I guess you could say the plants look "sheared". I do not ever trim the foliage.

Shearing is what you do to shrubs when you want a thick neat hedge, an artificial shape or a dense plant. Usually you do this by taking the hedge clippers to it and cut the whole plant flush into a row, ball, square, triangle-- whatever. Hollies are often trimmed this way. Some shrubs and plants look terrible treated this way and should be cut back instead since this forces all the growth on the tips and the middle of the plant suffers from lack of sunlight. In my opinion this is the most unnatural & artificial thing you can do to any plant. Corporate offices often have this done in formal plantings.

To cut back you cut out dead branches (or stems) or ones that are too long, crisscrossed, or older branches (or stems) to thin out the plant and trim some of outer stems at a leaf node for shaping. This leaves a natural plant shape and growth habit.

In early spring or late winter cutting back means cutting off all dead growth from the previous year on perennials and ornamental grasses, often people do it when they see new growth starting at the crown. In summer, some plants that get top heavy or lanky will benefit from cutting back 1/3 of the top growth to stimulate new blooms and leaves. Herbs are commonly cut back in this way around mid season.