Does overload count as a different spell or the same spell for the purposes of spell cost reduction?

Overload is an alternative cost keyword, defined in CR 702.97. When you cast a spell using its overload cost, you are still casting the same card — you are simply paying an alternative cost instead of the mana cost printed in the top-right corner. No new or different spell is created.

Because it is the same spell, any effect that reduces the cost of spells (e.g., Goblin Electromancer reducing instant and sorcery costs by {1}) applies to the overload cost just as it would to any other cost. CR 601.2f instructs you to apply cost reductions after determining the total cost, regardless of whether that total cost came from the normal mana cost or an alternative cost like overload.

One important nuance: if a cost reduction references paying the spell's 'mana cost' specifically (rather than its 'cost' or 'total cost'), it may not interact with an alternative cost. CR 601.2e clarifies that alternative costs replace the mana cost, so a reduction tied strictly to mana cost could fail to apply. However, generic reductions like Goblin Electromancer work fine because they reduce the total cost of the spell, not just its printed mana cost.

Concrete example: You control Goblin Electromancer and cast Cyclonic Rift using its overload cost of {6}{U}. Goblin Electromancer's ability reduces the cost of instant spells by {1}, so you pay {5}{U} instead. Cyclonic Rift is still just one spell; overload simply changed what you paid for it.