The tilt of the surface of an imaging element will induce coma aberration and tilt aberration.

Coma aberration – occurs when the spherical wave-front, from point object, is tilted (has an angle) compared to the surface of lens. The image of a point object is asymmetrical, resulting in a comet-like (hence, the term coma) shape with sharpness decreasing along the axis of aberration.

Tilt aberration – occurs when the spherical wave-front, from point object, is tilted (has an angle) or is decentered compared to the optical axis of the optical system. The image of a point object is brought to focus on the Gaussian image plane (that is defined by the paraxial, low-angle beams), but with a shift (transverse displacement).

Zernikewise mathematically they are orthogonal, so no direct relationship among them.

Now tilt is the Zernike Aberration Z[1,+-1] and coma is the Zernike Aberration Z[3,+-1] so they are directly below each other.

Now as stated before physically coma Aberration shall come in the presence of tilt Aberration as well.

In particular a physical tilt of the optical element use to induce tilt and coma aberrations (respect to the non-tilted orientation of the optical element).

Similarly a phsical decentration of the optical element use to induce tilt and coma aberrations (respect to the centred orientation of the optical element).

are you familiar with "Optics" by Eugene Hecht? It has a good chapter on aberrations, including coma, field curvature and distortion. The pictures help to visualize which aberration is which

I would agree with Samule that the nature of the two aberrations is fundamentally different; the origin of coma is proportional ot the size/dimensions of the object (eg spherical concave grating look at Namioka's publication in 1953) and it is there regardless the tilt

I think that it depends what you are considering. From a point of view of the wavefront, in both cases they imply an angle with the axis of the optical system. So that the zernike term of coma simulates a "mean tilt" of wavefront next to a tilt term. The question, as some people say you previously is that, in the image plane, the coma aberration shows asymmetry and tilt shows something next to defocus, prefocus in a side and postfocus from the other side of the image point.

Hans Buchdahl developed an extensive theory of geometrical aberration coefficients in which he addressed not only first order coma but also higher orders (Optical Aberration Coefficients, Dover Publications 1968).  He distinguishes between aberrations depending only on the angle of the object away from the axis of symmetry of the optical system (e.g. tilt or distortion) and terms depending on odd orders of that angle but also having an aperture dependence (various orders or types of coma).  Clearly , then, tilt and coma have different dependencies.  They are not necessarily orthogonal (since both depend on the position in the field of view, but coma has an aperture dependence that tilt does not.  If one chooses only to consider first (or Seidel) aberrations then distortion (or tilt) has no aperture dependence but a cubic dependence on tilt, whereas coma has a linear dependence on tilt and quadratic dependence on aperture (for image plane - lateral - measures of aberration rather than wavefront measures of aberration).  Happy to discuss further if you're interested.