Well.... Arcane vs Divine magic is defined on that sidebar on page 205 of the 5E PHB.
But practically to my knowledge you're right. There are no rules that come off Divine vs Arcane magic.
I believe some magic items care what *class* you are, but not what power source.
Personally I think 5E does a good job describing the different classes magic as quite different (even if mechanically they're pretty similar) and prefer not grouping them into the binary categories so that a Paladin's power is not intrinsically closer to that of a Druid than a Bard is.
Casters are defined as arcane or divine, not spells. The spells cast by the caster make them arcane or divine because of the caster and how he or she makes use of the magic. The only difference is divine casters require a direct intermediary to tap the magical weave while arcane casters tap that weave directly. Magic is simply stated as being the stuff of creation.
For example, a Bard is listed as arcane so when a bard casts cure wounds the bard is manipulating the weave directly in order to create the cure wounds effect. A druid casting cure wounds uses the divine forces of nature as an intermediary to access the weave in order to create the cure wounds effect. The weave, spell, and effect aren't different; only them method the spell caster uses to access each.
The sidebar indicates the magic matches the caster, but there's no mechanical difference in the spells and magic still comes from the same weave. The relevant mechanic is class. The arcane vs divine classification is fluff.
I would probably pattern a feat based on "pick one of the following classes" as per existing feats, and use one feat, if I were to look at something based on the traditional concepts.