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The Forgotten Realms was first published for AD&D 1st edition. When 2nd edition came out, the change in spells and available classes was explained through the Godswar aka The Time of Troubles.

The introduction of D&D 3e was exceptional in that there was no overarching, global in-setting event introduced to explain the rules changes. Oddly, the adventure Die Vecna Die! was intended to explain the rules changes (for all D&D settings), but its events were never made FR canon. WotC just proceeded with the 3e rules and setting changes without adding any corresponding historical events. The 3e change is thus “silent” in FR's historical record.

Karsus's Folly was made global setting canon with 3e as a historical detail that further developed the history of Netheril and explained some changes local to the Anauroch and some new game elements, but it wasn't the same kind of global upheaval—it was more of a retcon slipped in as undisruptively as possible.¹

The Spellplague (and about a century) explained the shift from D&D 3.x to 4e, and the Second Sundering did the same for the transition to 5e.

1. ^{Although Karsus's Folly was first described in a 2e adventure, the way 2e setting publishing worked meant that only the frozen-moment-in-time documented by the basic setting boxed set was canon. DMs were given explicit authority over what was canon beyond that. Thus changes made by adventures were only canon in a campaign if a DM used those in their campaign — because of course, the PCs might change the outcome! D&D 3e cemented Karsus's Folly as the official way it happened in Realms history for that revision of the base setting, so though it took place earlier, it wasn't canonised until 3e.}

In later D&D editions, the term eldritch is associated with the warlock class, whose signature class feature is eldritch blast. The warlock was introduced in 3.5e’s Complete Arcane, and was a core class in both 4e and 5e. All three of these warlocks tended to revolve around the use of eldritch blast, and as a result, feats and items specifically tailored for this class often use the word eldritch, and such things that are more generally for all arcanists tend to avoid it.

The warlock class is an arcane class, so eldritch can be seen as a subset of arcane. However, warlocks generally gain their powers not through study (as with wizards) or ancestry (as with sorcerers), but through pacts with fey, fiendish, or alien creatures. This accounts for the connotations and associations you’re seeing around the eldritch term.

However, the term is also simply an English word, and it is sometimes used in situations divorced from the warlock class even after it was printed (and clearly, prior to Complete Arcane, any use of the term had nothing to do with the class that hadn’t been written yet). This is seen perhaps most notably (to modern D&D, anyway) in the eldritch knight class; that was originally printed as a prestige class in the Dungeon Master’s Guide for 3.5, before Complete Arcane was printed. At that point, it was just used as more-or-less a synonym for arcane. And even though both 4e and 5e already had warlocks with associations with the word eldritch, Wizards chose to keep the eldritch knight name for an arcane-casting fighter, using it as a knight paragon path in 4e and a fighter archetype in 5e. So the eldritch knight could be seen as a big exception to the idea of “eldritch” being associated with warlocks. There are others.

However, even when used simply as English words, the words have different connotations. Arcane means complex and/or secret, and anything secret can have sinister associations, but eldritch highlights them. Something arcane may merely be complex and difficult to understand (quantum mechanics is very arcane), but something eldritch more strongly hints at something sinister going on.

For reference, Google provides the following definitions:

el·dritch

ˈeldriCH

adjective

weird and sinister or ghostly.

"an eldritch screech"

ar·cane

ärˈkān

adjective

understood by few; mysterious or secret.

"modern math and its arcane notation"