【Flow】 ,  【stream】 ,  【current】 ,  【flood】 ,  【tide】 ,  【flux】  are comparable when meaning something issuing or moving in a manner like or suggestive of running water.

【Flow】 may apply to the issuing or moving mass or to the kind of motion which characterizes it, but in either case it implies the type of motion characteristic of the movement of a fluid; the term may suggest either a gentle or a rapid pace and either a copious or a meager supply, but it consistently implies an unbroken continuity of the particles or parts.

【Stream】 implies a 【flow】 characteristic of a body of running water (as a river) or of water pouring forth from a source or outlet (as a fountain or a faucet). The term places emphasis more upon the volume, the duration, and the constant succession and change of particles than upon the type of motion.

【Current】  differs from  【stream】 in laying greater stress on the direction or course of the movement implied and in carrying stronger suggestions of its force or velocity.

【Flood】  is often used in place of  【flow】  or  【stream】 to imply extreme copiousness in the supply or to attribute to it an overwhelming or torrential power.

【Tide】 applies to something that flows or courses like an ocean 【tide】 and suggests either an alternation of directions or a power to suck one into its course by the force of its outward or inward pull.

【Flux】 , more specifically than  【stream】 , stresses the unceasing change in the parts, particles, or elements and, sometimes, in the direction of what flows.

【Flux】 often specifically applies to the outward aspect or appearance which is constantly changing in contrast to its real and abiding nature.