Eddy current losses are zero in ideal inductor. Now add secondary ideal coil, shorted, with finite resistance. This will work as transformer. There are two consequences, resistive loss and reduce of inductance of primary coil. For example in extreme case with fully coupled transformer and zero resistance, shorted secondary coil will subtract inductance completely, so the primary coil will become a zero ohm conductor with zero Henry.
Now replace secondary ideal coil and resistor with simple resistor in series with single ideal primary coil. You will get equivalent circuit, depicting nature of losses. These are thermal losses.
Another nonidealities is resistance of coil, even if it is an air coil. The reason Radio literature is talking about losses is not an energy concern, but the Q factor concern, because the filters made with lossy components will be more difficult to make as selective as ideal filters. Or perhaps if the topic is high power radio, then the losses are an energy concern too, together with selectivity.