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).
