Turn, revolve, rotate, gyrate, circle, spin, twirl, whirl, wheel, eddy, swirl, pirouette can all mean to go or move or cause to go or move in a circle.
Turn is a general rather colorless word implying movement in circle after circle or in a single full circle or through an arc of a circle. It is interchangeable with most of the other terms in their less specific uses.
Revolve may suggest regular circular motion on an orbit around something exterior to the item in question. It may refer to the dependence of the less important, the secondary, on something cardinal or pivotal which resolves or determines.
Rotate is likely to suggest a circular motion on an interior axis within the thing under consideration which may be not moving otherwise.
Gyrate may suggest the regularity of revolve , but it is more likely to be used to indicate a fluctuating or swinging back and forth which describes circular or spiral patterns.
Circle basically applies to a movement around in a more or less circular pattern, but it can also be used with reference to a lack of straight directness in a winding course or, specifically, to a curved or arched course followed in avoiding something.
Spin implies rapid sustained rotation on an inner axis or fast circling around an exterior point.
Twirl can add to the ideas of spin those of dexterity, lightness, or easy grace.
Whirl stresses force, power, speed, and impetus of rotary or circular motion.
Wheel may suggest either going in a circular or twisted course or turning on an arc or curve to a new course.
Eddy suggests the circular movement, sometimes fast, sometimes slow, of an eddy; it may be used in situations involving indirection, futility, or isolation from main currents.
Swirl suggests more rapidity, flow, or graceful attractiveness than eddy .
Pirouette suggests the light graceful turning of a ballet dancer.