In Logic, Circle and Vicious Circle are the same thing.
Outside Logic, the term Vicious Circle may be properly applied to "the reaction between two evils that aggravate each other: the wrecked sailor's thirst makes him drink salt water; the salt increases his thirst." (Fowler, Dictionary of Modern English Usage.)
But the term is often improperly applied to a state of things when two conditions exist side by side, or follow each other, and are only apparently connected by a causal relation. (See under Cause and Effect.) Drunkenness—poverty, poverty—drunkenness and armaments—war, war—armaments are often cited as vicious circles from which it is impossible to escape. The solution is—look outside the so-called circle for another condition, of which these two conditions are both effects : if that condition can be found and remedied, then both drunkenness and poverty, war and armaments will be obviated.
Another "vicious circle" is the gist of an argument often put forward as an excuse for inaction by those who are too comfortable to care about bettering others' social conditions. They say something like this:
"What's the use of all these schemes for slum clearance? You uproot these people from their drab and sordid houses in the slums, and plant them in a garden city. In a year or two you will find they have chopped up the banisters for firewood and are storing coals in the bath, and soon your vaunted model dwellings will be slums again."
Or this,
"I believe in improving the condition of the poor, but the trouble is that, if you make them better off, they only multiply faster, and thus keep themselves in their old condition of poverty."