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The two-component crystals formed from pyridine or 4-dimethylaminopyridine with maleic, fumaric, phthalic, isophthalic, or terephthalic acids were characterized by X-ray diffraction. The two-component solid forms involving pyridine included both salts and cocrystals, while 4-dimethylaminopyridine crystallized exclusively as a salt, in agreement with the differences in the pK a values. Five previously unknown salt solid forms of 4-dimethylaminopyridine and the crystal structure of a pyridine fumaric acid (2:1) cocrystal are reported. An in-situ base catalyzed isomerization of maleic acid was observed in cocrystallization experiments involving pyridine. The salts formed between 4-dimethylaminopyridine and fumaric acid included one or two fumaric acid molecules within the crystal lattice. Thus, the reported grid of crystal forms demonstrates the limitations of empirical rules for predicting the stoichiometry and covalent bonding of the acidic proton within salts and cocrystals. Many of the crystal structures displayed either the neutral or the ionic form of the carboxylic acid-pyridine heterosynthon, and the similarity in crystal structures between the neutral and the ionized molecules makes the visual distinction between a salt or cocrystal dependent on the experimental location of the acidic proton. Computational modelling experiments, by relocating the acid protons in the salts to produce cocrystals and vice versa, show that the crystal structure can be better modelled when the crystallographic designation of salt or cocrystal is used. Periodic electronic structure calculations also show that there is generally a significant energy penalty to relocate the acidic proton, which is considerably reduced when experiments indicate the presence of disorder in the acidic proton position.