Straight Stairs

Straight Stairs are just that straight. They can have different landings.
Flared Stairs

Flared stairs actually flare out at the bottom. The stair tread are all straight but the sides of the stair will curve out. They can flare on one side or both.
Curved Stairs

Curved stairs will curve in a circle and will have 2 sides.
Spiral Stairs

Spiral stairs have all their tread rotating around a central point.