I do not think thisThis is not a merely linguistic question since it seems obvious that motivation and desire and motivation fulfil logically different roles in the explanation of action.
Desire connects with motivation at least in this way: If I did an intentional action, say I bought a packet of cigarettes without coercion or constraint, then it makes sense to ask what my motivation was in buying the cigarettes. Didn't I realise the health risks associated with smoking ? Why did I buy the cigarettes? When you have answered the 'why?' question, then you know my motivation. A standard model, going back at least to Hume, has it that the motivation for my intentional action involves a belief and a desire. I bought the cigarettes because I believed they were available and because I desired to smoke them. On this approach, desire along with belief is one of the elements that explain why I did a particular intentional action, in other words a specific desire constitutes one part or element of my motivation where a specific belief constitutes the other. If desire constitutes a part or element of motivation then they are on different logical levels.
It isn't the case, though, that desires invariably motivate. I can have a desire to smoke a cigarette and yet repudiate that desire. I have a desire to smoke but also a stronger desire not to smoke. If a desire can be present without a motivation then again they are logically distinct.
Desires can also fail to form and hence to motivate if a certain belief is absent. If I believe that the building in which I am working is on fire, then I am very likely to have a fire-avoiding desire to quit the building. However, the building can be blazing within inches of my office yet I will have no fire-avoiding desire to quit the building if I have no belief that the building is on fire. One way of describing this kind of case is in terms of a distinction between dispositional and occurrent desires. I have, let us asssume, a dispositional desire to quit burning buildings - a prospensity to form desires to quit such buildings - but there will be no occurrent desire, no desire to quit this building now, unless I believe (as I may well not) that the building is on fire.