I agree with lifecollage: I would use "porch" for what she has -- although I might not think it strange if I heard someone else call it a balcony. I use "balcony" for a structure with a smaller area and no roof. In my mind, a porch has a roof, and the differences between balconies, decks, and patios are in the height above ground and the square footage. Actually, I think a large-area outdoor living area with no roof would be a deck even if it were multiple stories up, or I might call that a porch as an umbrella term. I think a patio must be at ground level and have a tile or flagstone surface and no permanent roof.

I asked this one because my mother-in-law calls her back porch "the patio" and I wondered whether that's a regionalism. But maybe I don't have any eastern-midwest natives here to query. The funny thing is, she has a flagstone-paved area on the ground near "the patio" but I don't think she calls that a patio.