is that sonics is the science and technology of sound while conics is that branch of geometry which treats of the cone and the curves which arise from its sections.

As nouns the difference between hyperbola and conics

is that hyperbola is (geometry) a conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone while conics is that branch of geometry which treats of the cone and the curves which arise from its sections.

As nouns the difference between geometry and conics

is that geometry is (mathematics|uncountable) the branch of mathematics dealing with spatial relationships while conics is that branch of geometry which treats of the cone and the curves which arise from its sections.