What's the difference between a terrace and a patio if we are talking about something related to house.

They have pretty much the same meaning, relative to a house. The word 'terrace' has more meanings, though, than 'patio'. See: http://www.thefreedictionary.com/terrace
I think a "patio" is meant to be inside the house, a roofless area, with plants, opened to the sky and the sun, surrounded by parts of the house at least on 3 sides. To me a "terrace" has its backside against the house, and opens onto a garden, a pool-area, or the street, if it's a restaurant or a café.
Students: We have free audio pronunciation exercises.

Interesting. In the United States, patios are normally outside.
Students: Are you brave enough to let our tutors analyse your pronunciation?
No, not here. I have one, it's surrounded by a blind wall on one side, and by the kitchen and the "PC room" on the 2 other sides, both with French (what else?) windows to allow access. The remaining side opens on to the garden. It's got no roof, but a few beams with some climbing plants. It's a kind of "garden enclave" in the house. Here, a "terrace" is a tiled area, the backside against the house. I think it's the same in Spain, Morocco, etc...