I was wondering since the Bard has a lot of spells that don't seem to have him using his instrument to perform, are there 2 different types of spells for the Bard, Normal magic spells and Instrument Spells? Or is the Bard really using an instrument to cast those spells but it just doesn't say?
Bards can use musical instruments as their spellcasting focus (PHB 53). A character can use a spellcasting focus to replace Material components needed for a spell (with some restrictions, PHB 203). Thus a bard only needs to use an instrument when he casts a spell with a Material component. Whether he has to play the instrument is a different question, though.
As Miniman pointed it out, you can forego the use of instruments even on these spells if you use a component pouch.