In 2D, there is the regular circle and the oval. In 3D, there is the sphere (I am not entirely certain this a considered a circle though).
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no; for example, a circle and a circle within that circle have no common tangents.
they are both types of shapes
Two different types of shapes would be a circle and a square. they differ from each other in the fact that a circle's shape is perpetual as a square has four equal sides and four corners.
an ellipse, one of the four types of "conic sections": ellipse, circle, parabola, and hyperbola
Trigonometry based on a unit circle and radians and trigonometry based on a right triangle.