The ellipse is the locus of points such that the sum of distances from the foci is constant, while the hyperbola is the locus of points for which the difference between the distances from the foci of a point is constant
The thing in common, as a place of puinti, is that you use to call it, a transaction between the distances of a point and foci.
Instead of the hyperbole, the ellipse may degenerate into another locus of points: the circle, which is an ellipse whose axes are equal, ie the eccentricity 1
It hyperbole that the ellipse are so called "conical" or figures generated by the intersection of a cone with a plane, slightly inclined with respect to a vertical axis, for the ellipse, while totally tilted to a hyperbola.
Ellipse : locus of points which moves such that sum of the distances from two fixed point is constant.
Hyperbola : locus of points which moves such that differences of the distances from two fixed point is constant.
Ellipse : two focci, two axis ,major and minor, closed and bounded region ,four vertices and centre
Hyperbola : two focci, two axis ,transverse and conjugate , un bounded region ,two vertices and centre.
Ellipse : eccentricty less than one.
Hyperbola : eccentricity more than one.