Hi Sleepseek,
If anything, I think that pillows are probably "harder" to fit than mattresses because preferences and feel, and even moods, weather, sleeping environment and time of year play an even bigger role and this is a personal choice for each person. Some people have a "menu" of choices that they can choose according to changing preferences.
The objective part is that the cervical spine (neck) needs to be supported in its natural alignment. Side sleeping needs thicker (to hold the head up and fill in the larger gap between the side of the head and the mattress and support the head and neck), back sleeping needs a little thinner and possibly with some additional thickness, contouring, or firmer zoning under the neck), and stomach sleeping needs very thin or none at all (just enough softness for comfort but not enough to hold the head up and bend the neck back or sideways).
Multiple sleeping positions may need to be "in between" or be adaptable or adjustable such as pillows that can be "shaped" or "scrunched" (unlike solid foam pillows). The goal is to support the neck and head so that the cervical spine is in alignment and supported when completely relaxed. Larger body frames or firmer mattresses where the gap between the sleeping surface and the head and neck need more loft or firmness for side sleeping. Back sleepers and to a lesser degree side sleepers often choose an anatomic pillow which is either shaped higher or firmer on the edges and lower or softer in the middle to help fill in and support the natural curve of the neck.
The subjective or preferences part is how it "feels" while it supports you and keeps your head and neck in alignment and this is very subjective and individual.
Temperature is also an important part of pillow choices and more breathable materials and materials that can wick moisture and humidity away from the skin will tend to be cooler than materials that are less breathable and moisture wicking.
How soft it is, how "scrunchy" it is, how hot/cool it is, how "dead" or "lively" it is, how firmly it keeps your head in place, how it feels against your skin, and even how noisy it is (as in buckwheat hulls), how "natural" it is, and how it smells are all part of the choices that each person makes (and often remakes many times because needs and preferences can change over time and with changes in external conditions)
Some of the options for materials includes down, feathers, memory foam, shredded memory foam, wool, cotton, latex, shredded latex, silk, flax seed, kapok, buckwheat hulls, millet hulls, various synthetic fibers, gels, water, and various zoning options, shapes, variations, and combinations of all of these.
Most pillows come with recommendations for the sleeping positions they are best suited for but as long as it does what it has to do ... the rest is sometimes a "lifetime" adventure ... and for some people changes as often as their moods

.
Part of the fun (or sometimes frustration) of pillows is that its as individual as our taste in clothes ... and as long as we get the basic "size" and shape and firmness right so that the neck and head is in good alignment in all our sleeping positions over the course of the night ... the rest is all about our preferences.
Phoenix
PS ... now that I've got all that out of the way so I can deny I ever made a pillow recommendation to anyone ... a good thin pillow might be down because its really soft and flattens more than most materials.