The phrase "obvious distinction" is correct and usable in written English.
You can use it when you want to emphasize that the difference between two things is clear and not hard to recognize. For example, "There is the obvious distinction between the two types of cars, which makes it easy to tell which one is the luxury model."
There is an obvious distinction, however.
Now, this is an obvious distinction and an important distinction.
A further obvious distinction is to have a test of maximum practical pressure differential.
Between the first two of these, there is no obvious distinction in terms of empty weight.
This concert is typical in bringing together choruses of no obvious distinction from around the country.
The illusion vanishes when the rather obvious distinction it obscures is recalled.
Moreover, the explicit solvent simulations demonstrated obvious distinctions in dynamic behaviors of water, such as their residence behaviors and hydrogen bonding.
One of the most obvious distinctions is whether services allow users to see what other people are listening to, to read over their playlists and compare their favorites.
There are obvious distinctions to be drawn between the C.I.A.'s "stress and duress" and the horrors of Saddam's dungeons in their purposes (aborting terror attacks versus maintaining a tyranny) and, more important, in their degrees of cruelty.
The basic problem is that Mr. Johnson is a good deal readier to see hidden similarities -- between, say, the nature of the former Soviet satellite East Germany and the American "satellite" Japan -- than to admit obvious distinctions.
There are obvious distinctions to be drawn between the C.I.A.'s "stress and duress" and the horrors of Saddam's dungeons — in their purposes (aborting terror attacks versus maintaining a tyranny) and, more important, in their degrees of cruelty.
