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Number of vertices and number of triangles in modern game

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No, vertices can be shared between adjacent triangles, as long as all attributes match (position, normal, uv, whatever). For example, vertices along a 'hard edge' (not shared normals) are not shared between adjacent triangles. At maximum, numVertices = numTriangles*3, but there is as much sharing as possible.

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You always have more vertices than triangles (assuming all your geometry is made up of triangles), but it is possible to reuse vertices between triangles (by having all triangles with a common vertex or by having consecutive triangles share 2 of their vertices) so there can be less than three vertices per triangle.

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