Madame de Rênal loves without knowing that she loves, and she follows her heart. Mathilde de La Mole decides to love and needs reasons before letting her heart be moved. The one acts from impulse, the other from a plan.
Julien himself states the difference, in Chapter XXX of Book Two, while resisting Mathilde: "Madame de Rênal found reasons for doing what her heart dictated; this young lady of high society lets her heart be moved only after she has found good reasons for it to be moved." The narrator has already given the second type a name: Mathilde's love is "cerebral love," which "knows itself too well" and judges itself without cease.
The difference shows in the gestures. Under the linden tree, Madame de Rênal "was not thinking of anything, she let herself live." Mathilde summons Julien to her room as a proof of courage, despises him as soon as she knows she is loved, and yields only when he treats her with calculated indifference, following the method of Prince Korasoff. With one, Julien comes to forget to pretend; with the other, he advances only by pretending.
The ending shows which of the two Julien returns to. In prison, Mathilde's heroic devotion wears him out. According to the narrator, he "was tired of heroism," and it is to Madame de Rênal that he says he will never have been so happy. The two take leave of each other in opposite ways: Mathilde with a ceremony around the head of her lover, Madame de Rênal with a silent death.