Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra M. We show that the differential calculus, generated by the maximal subalgebra of the derivation algebra of M that can be related to infinitesimal symplectomorphisms, gives rise to a natural construction of Yang-Mills-Higgs models on M and a natural interpretation of the covariant coordinates as

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... fields. We also compare in detail the main mathematical properties characterizing the present situation to those specific of two other noncommutative geometries, namely the finite dimensional matrix algebra M_n(C) and the algebra of matrix valued functions C^∞(M)⊗ M_n(C). The UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also discussed.