Non aromatic compounds, as the name implies, are not aromatic due to reasons such as lack of planarity or disruption of delocalization. They may contain 4n or 4n+2 π electrons.
Antiaromatic compounds are planar, cyclic, conjugated systems with an even number of pairs of electrons. Such compounds satisfy the first three criteria for aromaticity. i.e. they are planar, cyclic with an uninterrupted ring of p orbital bearing atoms. But they have an even number of pairs of π electrons (4n, n = 1, 2, 3 etc). It should be noted that an aromatic compound is more stable compared to an analogous cyclic compound with localized electrons, where as an antiaromatic compound is less stable compared to an analogous cyclic compound with localized electrons (in 4n+2 systems delocalization increases the stability where as in 4n systems, delocalization decreases stability)
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