The most obvious difference between climbing indoors and outdoors is the lack of multi-coloured holds on rock outdoors. All the handholds and footholds are the same drab grey/brown colour. So even working out what a hold is may take a little while to 'get your eye in'.
But there's more to it than that. Indoor climbing walls are great at what they offer, but the overwhelming majority of routes and holds are based on jugs and crimps. The indoor world has very little in the way of blank slabs, cracks (especially jamming ones), bridging moves and so on. Climbing on real rock can feel very different.