I feel like these two speeches have some things in common like how they're both striving for something in the name of love but I'm not too sure. What are the similarities and differences between the two speeches?
You can see the Introduction to Plato's Symposium (Sheffield & Howatson editors), Cambridge UP (2008), for an overview of the various speeches of the dialogue.
"Phaedrus, the first speaker, puts the issue of the role of love in moral education firmly on the agenda. He argues that a love relationship has the greatest power when it comes to acquiring excellence (arete) and happiness, as he conceives of such things. [page xi]"
"There is, Socrates supposes, an end, or a greatest good, towards which our desires and actions ultimately aim. What we really want as desiring agents is the possession of the sort of good that will satisfy our desire for happiness. This reflection suggests to Socrates that people are mistaken to suppose that eros refers to sexual desire exclusively; in fact, it is happiness quite generally that is desired and sexual desire is just one way in which this broader aim is manifested. [page xv]"
"One thing that is clear is why Socrates’ account will move from an analysis of the nature of such desire to an account of knowledge and its acquisition; for if we all have a desire for our own good and happiness, the issue becomes how to identify correctly the nature of this good. [page xvi]"
See also Plato on Friendship and Eros.