Is there really any difference between Resonance and Mesomeric effect?

Have you read the poem "Five Blind Men and the Elephant", where each person tries to explore an elephant and comes with their own version. Someone touches elephant's trunk and calls it a snake, someone touches the legs and calls it a tree trunk and so on. The world of molecules and sub-atomic world is indeed that elephant, and chemists are unfortunately unable to see them- to see what is happening. Hence each one comes up with an intelligent story only to be improved or discarded later. So the lesson is that don't take everything literally (incuding the statements made by high school or college teachers). Moreover, do not rely on the web-answers including this one ultimate facts.

In the same way the concept of resonance was developed really a long time ago. Keep in mind that none of the structure you draw with resonance reflects a reality. It is a subtle and an esoteric way of human expression that we do not know how it looks like in reality. X-rays allow you see the arrangement of solids in space but it does not let you see electrons, there is no physical arrow pushing going on and there no electron dance going on. It is all human imagination.

Think of the classic benzene example, (image from Wikipedia). None of the structures reflect a reality, hence the term resonance hybrid, because benzene does not chemically behave as if its double bonds were "static". The C-C bond distances in the ring have to be different, otherwise.

There is a very nice article by Robert C. Kerber titled If It’s Resonance, What Is Resonating? in the Journal of Chemical Education (It is freely available on Google Scholar). Have you wondered why the name "Resonance"?

History The use of multiple structures to represent compounds with (what we now call) delocalized bonding (4) was pioneered in Germany by Arndt (5) and in Britain by Ingold (6). Their ideas were based essentially on chemical intuition. In the United States, Pauling $(7,8)$ in his pioneering applications of the principles of quantum mechanics to chemistry, came to a similar description from a different starting point. Whereas the concepts of describing a single substance in terms of multiple structures may not have differed significantly, the terminology did. Arndt coined the term $Zwischenstufe$ for the hybrid structure, while Ingold opted for the equivalent term (derived from Greek) mesomer. He proposed for the concept the terms mesomeric effect or mesomerism. The cognate term mesomerie came into use in French and German. Pauling preferred the term resonance, derived from valence bond theory (see below). Pauling and Ingold were well aware of each other's terminology, and each offered reasons for rejecting the alternative proposal: Because the resonating system does not have a structure intermediate between those involved in the resonance, but instead a structure which is further changed by the resonance stabilization, I prefer not to use the word 'mesomerism,' suggested by Ingold, for the resonance phenomenon.

• L. Pauling (9) Pauling describes the phenomenon under the name 'resonance,' which, as is well known, is based on the mathematical analogy between mechanical resonance and the behavior of wave functions in quantum mechanical exchange phenomena. There appears, however, to be some possibility that this method of description may suggest an analogy which has never been intended.
• C. K. Ingold (6) Pauling's argument conflates the concepts of structure and energy. Moreover, his chosen term resonance is derived from an analogy to coupled oscillators, which also lacks energetic implications: "There is no close classical analogue of resonance energy" (10). So neither term includes explicit reference to energy considerations, weakening Pauling's argument. For use in discussing the structure (i.e., geometry) of the hybrid, Ingold's argument seems the more persuasive. His recognition of the gratuitous oscillatory aspect of the analogy is prophetic of the subsequent experience of generations of students.*

Your next query on mesomerism and IUPAC. In terms of terminology, most chemists follow the IUPAC recommendation's on terminologies. You can call mesomerism as a type of resonance. See this reference "Introductory Organic Chemistry and Hydrocarbons: A Physical Chemistry Approach" by Caio Lima Firme on pg 111-112.

As Ingold himself defined: "Mesomerism is an extension of valency theory (that is the classical valence bond theory) and, like all valency theory, is founded in the quantum theory (...). The fundamental wave-property in the theory of valency is resonance $-$ the resonance of connected standing waves; their mutual perturbation replaces these waves by new standing waves" (Ingold 1938). Ingold exemplified the resonance theory by using the two resonance structures: $\mathrm{R}_{2} \mathrm{~N}-\mathrm{CH}=\mathrm{N}^{+} > \mathrm{R}_{3}$ and $\mathrm{R}_{3}^{+} > \mathrm{N}=\mathrm{C}(\mathrm{H})-\mathrm{NR}_{2}$ with their own standing waves which resonate to form the real molecule. Ingold stated that the term mesomerism was given to account for the special importance of resonance in organic chemistry. He also said: "When mesomerism was first recognized as a general phenomenon in organic chemistry, it was appreciated as an electron displacement than as an energy disappearance" (Ingold 1938). From this point on, we can say that mesomerim is equivalent to resonance type 3 (resonance involving only charged and/or neutral covalent structures), although IUPAC recognizes mesomerism as essentially synonymous with resonance (which could include all types of resonance). Nonetheless, IUPAC adds that mesomerism is "particularly associated with the picture of $\pi$-electrons as less localized in an actual molecule than in a Lewis formula” (IUPAC Gold Book). Then, mesomeric state is the same as resonance hybrid and energy of mesomerism is synonymous to resonance energy (Ingold 1938).