Changeable, changeful, variable, mutable, protean are comparable when meaning having or showing a marked capacity for changes or a marked tendency to alter itself or be altered under slight provocation.
Changeable, the ordinary and most comprehensive term of this group, usually suggests this as a characteristic or property that is the result of such reactions as inconstancy, fickleness, an unsettled state, a ready responsiveness to certain influences, or a roving habit.
Changeful is a more poetic term than changeable; it throws greater stress on the fact of changing frequently than on the underlying characteristic or property which manifests itself in such changes.
Variable carries an implication of subjection to frequent and often deeper changes than either of the preceding words; it stresses shifting or fluctuation as a characteristic or property and therefore usually connotes uncertainty or unpredictability.
Mutable also implies subjection to change, but it suggests an opposition to unchanging, fixed, or permanent and therefore is less often applied to something fluctuating and variable than to something living, growing, or developing that shows changes due to progression or retrogression or to external influences or conditions over which the thing affected has no control.
Protean suggests a capacity for assuming many different forms or shapes without loss of identity; the term therefore implies changeability with respect to outer manifestations rather than inner character or nature.