Verse, stanza both mean a unit of metrical writing.
Verse is both wider and more varied in its popular usage since it can denote a single line of such writing, such writing as a class, or, along with stanza , a group of lines forming a division of a poem and typically following a fixed metrical and sometimes rhythmical pattern.
Verse may also specifically denote the part of a song preceding the refrain or chorus or a comparable part of an anthem or hymn.
But in technical use and in discussion of prosody verse is restricted to the single line of metrical writing and stanza is regularly employed for the group of lines that forms a division of a poem.