Which isn't exactly correct either; a (nonideal) transformer with shorted secondary has no losses, and inductance equal to the leakage (= L1 - M).
Somewhere inbetween zero ohms (short) and infinite ohms (open, a lossless inductor) lies a true lossy inductor.
Physically, the core (and its losses) are usually tightly coupled to the winding, so the leakage reactance is small with respect to the loss resistance, and thus, a nonideal transformer model isn't critical, and the losses can be modeled reasonably well as a parallel equivalent. A series equivalent is sometimes useful instead.
I have a nonideal, nonlinear (saturable), lossy transformer model I like to use for switching design. All the parameters are to hand, so you don't have to specify an equivalent, it does it from the differential equations directly.
To further expand on the concept of lossiness, general core materials (inductive and capacitive) are defined by an infinite number of parallel branches, consisting of series RLCs (or the reciprocal, an infinite series chain of parallel RLCs). This general approach allows one to model frequency-depending loss, dispersion, resonance, filtering and so on. Ferrites typically have a cutoff frequency, beyond which they appear resistive (i.e., imaginary permeability -- a "flux capacitor", as it were). Ceramic capacitors behave identically; the electric/magnetic domains in both materials take some time to "flip" to the new state and thus contribute hysteresis, eddy current (or equivalent) and resistance to the response. Some particularly interesting materials continue to do the flippity-flop out into optical bands, where some very interesting things occur, from simple coloration all the way up to cloaking (not that we have visible light metamaterials yet, but microwave materials have been fabricated!).
Tim