Liquefy, melt, deliquesce, fuse, thaw are comparable when they mean to convert or to become converted to a liquid state.
Liquefy, the general term, is applicable not only to solids but also to gases.
Melt basically implies slow liquefaction, usually through heat; the term commonly suggests a softening, a loss of shape, and a running consistency. In its frequent extended use melt is applied to masses that are gradually dispersed or grow thinner or more tenuous and finally disappear or to persons or their emotions or reactions that grow softer, gentler, or more tender or to tones, colors, and sounds that have a liquid quality and merge imperceptibly with others.
Deliquesce implies a disappearing by or as if by melting away and applies especially to gradual liquefying through exposure to the air and the absorption of moisture from it <hygroscopic salts that deliquesce in moist air> or to plant structures (as mushrooms) that liquefy in their decay. In its extended use deliquesce stresses loss of coherence rather than disappearance.
Fuse (see also MIX ) may sometimes replace liquefy or melt, but more often it stresses union (as of two or more metals into an alloy) by or as if by the action of intense heat. In its extended use, too, fuse stresses union.
Thaw may specifically replace melt in reference to something (as ice or snow) that is frozen or in extended use to something (as a cold heart, a cold disposition, or extreme reserve) equally stiff or rigid.