I have never actually did this myself, so I never questioned this.

My friend said that you cannot activate a spell card the same turn that it was set.

Is this true? I know this applies to traps, but what about Normal Spell cards and Quick-Play spell cards? Can I set and then later activate them during my same turn?

Normal, Continuous, Equip, and Ritual Spell cards can be activated the same turn they are set, unless an effect such as Anti-Spell Fragrance prevents you from doing so.

However, if you set a Quick-Play Spell, you cannot activate it the same turn.

Field spell cards can be activated the same turn they're set as well, I believe.

Oh yes, I forgot about those. Basically, I meant every non-Quick-Play Spell can be set and activated the same turn.