Cadaver/corpse/body for a dead human body

Corpse and cadaver are both medical/legal terms for a dead body. I would not call them degrading per se, but perhaps dehumanizing, and that is not necessarily for ill intent: we use clinical and legal terminology to be precise as well as to avoid emotional or cultural connotations of alternative terms that can be a distraction (e.g. pinna as opposed to ear, vertebral column as opposed to backbone).

Although cadaver is the older word, it has come to refer in particular to a dead body used for medical or scientific purposes, for example, for medical students to dissect, while corpse is used more generally. I do find corpse to be somewhat more evocative than simply dead body, as it brings to my mind an embalmed dead body, or the reanimation thereof, but that is likely the fault of too many zombie films.

A more elevated alternative would be remains, and remains which have been elevated for religious purposes are termed relics.

If on the other hand you did want to disrespect the dead, you could call the dead body a carcass, the word for a dead animal body used for food, whether processed by abattoir or buzzard. Etymonline says it is "not used of humans after c.1750, except contemptuously."

I work with police reports in teaching technical writing skills, and from reading a number of those, the distinction I commonly see (dealing with the same body) is...

The police officer finds the dead body/body at the crime scene.

The pathologist autopsies the cadaver.

The corpse is what gets buried.

In crime reporting, no presumptions are made in advance, so, upon arrival at the scene, a cop will likely not call a body a "dead body" unless there is indisputable proof. That rules out cadaver and corpse, and sometimes dead body, for the purpose of crime scene investigation.

As another answer notes, and the definition of the word commonly attests, cadaver implies a human body and is reserved for medical contexts: autopsies, dissections, and the like; and so its use is closely related to a specific context: hospitals, med schools, morgues.

Corpse, which also has the meaning of "something no longer useful" or "remains", is the least useful, descriptive, even humane of the three words, and perhaps this is why it's most common in the context of the thing that gets buried. Although redundant, dead body works in this context too.