"Damage Roll" doesn't have a hidden meaning
It just means any roll of damage dice. The rules don't actually say about "damage rolls", the terms "damage" and "damage dice" are used instead:
- "damage" — a numeric quantity with a specific damage type
- "damage dice" — any dice which are used for calculating damage
These terms are described in the "Damage Rolls" chapter, but "Damage Rolls" is just a name of the chapter, not a specific kind of rolls:
You roll the damage die or dice, add any modifiers, and apply the damage to your target.
See also Does "flat" damage count as a "damage roll"?
The PHB indeed has a few mentions of "damage rolls" or "weapon damage rolls", but they mean nothing special but rolling some damage dice. Compare this to an explicitly defined kinds of rolls:
Ability checks, attack rolls, and saving throws are the three main kinds of d20 rolls
Both damage and damage dice can be modified in some cases. "Damage dice" are doubled when there is a crit. "Damage" can be doubled or halved depending on resistance/vulnerability. Since addition is commutative, you can roll damage dice in any order, either sequential or simultaneously — the result will be the same.
The only case when it does matter is the Instant Death (a.k.a. "massive damage") rule. But this doesn't depend on what a "damage roll" is, it just depends on damage itself. See Is damage from multiple damage types cumulative for death and massive damage?
Critical Hits description is a bit inconsistent
The generic rule is:
Roll all of the attack's damage dice twice and add them together.
One can think only weapon damage dice should be doubled. However, spell attacks can score a critical hit. Features like Sneak Attack can deal double damage as well. The PHB says about this explicitly in relevant chapters. See See How does extra damage work for critical hits?
