In The Canterbury Tales, what are the similarities and differences in the themes of the knight's tale and the miller's tale in relation to love?
The Knight's Tale and The Miller's Tale (both of which are in Group A of The Canterbury Tales) share only one meaningful similarity--they are both told by pilgrims on their way to Canterbury.
The Knight, who represents the minor aristocracy among the pilgrims, tells a tale that reflects his class: an epic romance based on Boccaccio's Teseide (ca. 1340), the subject of which is Theseus and the rivalry of two cousins, Palamon and Arcite, for the hand of Emelye, the sister-in-law of Theseus. The Miller, on the other hand, represents (at best) the yeoman or middle class in medieval England, one step above the peasant class, and his tale is in the fabliaux tradition. Fabliaux are humorous (but using coarse humor) stories often centered on sexual misdeeds among what we would call the middle or working classes. Whereas the subject of The Knight's Tale is Palamon and Arcite's courtly pursuit of Emelye, who, by the way, doesn't even know she is the object of their affection, The Miller's Tale is about a young scholar who fools the old husband of a young woman so that the scholar and the young woman can act on their lust for each other.
The Knight's Tale focuses on the struggles of Palamon and Arcite to win Emelye's hand and, because this part of the tale is based on the chivalric romance, Palamon describes Emelye in very conventional romance terms:
I do not know whether she is a woman or goddess,/But I think she must be Venus (Fragment I: 101-2)
Comparing Emelye to a goddess keeps Emelye on an unattainable plane and is a typical chivalric romance theme--the unworthy lover strives to attain the god-like woman. Palamon's comment sets up one of the important disputes between the cousins. Arcite responds to Palamon by pointing out that Palamon's feeling is based on "the love of a goddess ("hoolynesse"),/And my love is for a living creature--in other words, Palamon is in love with an ideal, and Arcite is in love with a real woman.
When we arrive at The Miller's Tale, which is probably the funniest story Chaucer wrote, we enter a world in which lust, not love, is the guiding light for the characters. In this tale, Nicholas, the young scholar, weaves a skillful lie (that Noah's flood is on the way) to get the miller out of the way so that Nicholas and the miller's young wife, Alisoun, can make love. As a contrast to Palamon's description of Emelye, we have Nicholas' description of Alisoun:
She was as skittish as a jolly colt,/As tall as a mast, and straight as a bolt [an arrow] (Fragment I: 3263-64)
The idealism of the chivalric romance is not at work here, but plain physicality is, and the focus on naturalism and human physical nature points up the great difference in the two tales' approach to love.
In sum, then, love in The Knight's Tale is spiritual, embodying the conventions of the medieval romance tradition, but love in The Miller's Tale is purely physical and the product of lust rather than ideals.