Pour, stream, gush, sluice are comparable when they mean to send forth or cause to send forth copiously.
Pour usually suggests an abundant emission of what is sent forth, but it sometimes implies a coming in a course or stream, usually a continuous stream (as from a mouth, a spout, an orifice, or a wound).
Stream suggests a flow that is circumscribed (as by issuance through a course or from an opening), though it also may connote abundance or continuousness in that flow.
Gush implies a sudden and copious emission of or as if of something released from confinement; it often connotes a coming in a jet or in spurts.
Sluice implies the operation of something like a sluice for the regulation or control of the flow of water; therefore the verb sluice suggests a sending of water or liquid over a surface in an abundant stream.