Nowadays, a line of poetry is most commonly called just that, a line. A line can be identified as the string of words before a break, even if a sentence is not complete before the break occurs. A line is not the same thing as a sentence in poetry because poets arrange the lines for many different aesthetic reasons, and the line may or may not contain punctuation.
The arrangement of lines on the page, or typography, is often, but not always, arranged in stanzas of a certain number of lines. For example, a two-line stanza is a couplet, a three-line stanza is a tercet, a four-line stanza is a quatrain, and so on. Exceptions to stanza form include free verse, which intends to mimic the cadence of human speech and may consist of a single stanza.
Strictly speaking, a line is a unit of language into which the poem is divided.