What are the similarities and differences between the relationship between Touchstone and Audrey and the relationship Orlando and Rosalind?
Orlando and Rosalind demonstrate what is known as courtly love. Bother were born into some class of nobility, and there is an order and process to the way in which they court each other. They are shy about their love (Orlando's inability to talk to Rosalind after winning the wrestling match, her gift of the gold chain to him), until they find themselves in the woods. Rosalind is more bold in her ability to speak with Orlando when disguised as Ganymede. Orlando is more able to express his love for Rosalind, posting love notes on trees. Similar to Romeo and Juliet, their love seems to be all consuming, almost obsessive and based on very little knowledge of each other.
Similarly, Touchstone and Audrey's "love"--if it can be called that--is based on physicality. Touchstone, who has been at court and has a great deal of wit about him, is able to play around with Audrey's words and her desires in order to get her to marry him. This is similar to Rosalind's deception of Orlando--Rosalind uses her boy form to encourage Orlando's love. However, Touchstone simply wants Audrey to marry him so he can get her into bed--he has enough morals to marry her, but only for a physical desire. Orlando and Rosalind seem to have more than a physical attraction to each other.
Audiences would see Rosalind and Orlando's love as pure, good and courtly. Touchstone and Audrey would seem bawdy, unrefined and completely physical.