What is the difference between segirðu and ertu að?
Segirðu and ertu að both mean "are you," correct?
DANIEL Sæl Ewa. (Hello Ewa)
EWA Sæll. Hvað segirðu gott? (Hello. How are you?)
DANIEL Bara allt gott. (All right.)
Hvað ertu að gera í dag? (What are you doing today?)
EWA Ég er að vinna í dag. (I am going to work today)
En þú? (And you?)
DANIEL Ég er að læra íslensku. (I am studying Icelandic)

I am confused because segirðu and ertu að are both used as "are you."
I thought it mean that one is long term and the other is short term but they are both short term in this example.**I thought it meant that one is long term and the other is short term but they are both short term in this example.

Question

What is the difference between segirðu and ertu að?
Segirðu and ertu að both mean "are you," correct?
DANIEL 	Sæl Ewa. (Hello Ewa)
EWA 	Sæll. Hvað segirðu gott? (Hello. How are you?)
DANIEL 	Bara allt gott. (All right.)
Hvað ertu að gera í dag? (What are you doing today?)
EWA 	Ég er að vinna í dag. (I am going to work today)
En þú? (And you?)
DANIEL 	Ég er að læra íslensku. (I am studying Icelandic)

I am confused because segirðu and ertu að are both used as "are you." 
I thought it mean that one is long term and the other is short term but they are both short term in this example.**I thought it meant that one is long term and the other is short term but they are both short term in this example.

Answer

Although I am still learning, I think I might be able to help you.

I think there is a translation problem there. "Hvað segirðu?" is used as an expression to ask "how are you?", but the litteral translation is "what do you say?" (the infinitive is "segja" [sagði, sagt], to say).

While, as you said, the continous form "ertu að" comes from the verb "vera" [er; var, voru, verið], which is plain "to be".

Hope this helped, good luck! =)

Answer

@Leif Thorleifs
Thank you so much! You are from Iceland, correct? I was wondering if you could answer another question of mine, It's titled "Things I should not do in Iceland." I want to make sure I'm not rude to anyone when I'm there. Thank you again :)

Answer

Ert-u? Ert þú ?... same meaning, but ERTU is the lazy one, like RU? in english. You should say "ert þú" and you will earn respect ;)

Answer

We say " hvað segir þú gott? Segir ÞÚ and segir-ÐU ... the same word. ÞÚ becomes ÐU. Segirðu is a lazy icelandic style;)

Answer

It's like aekke_naekkepenn says. "Ertu" is ert (are, for 2nd person singular) + þú (you, 2nd person singular), literary it means "are you". And "að" means to, like "to do something". The other one is just translated to the correct English form of "how are you". It's like "what's up", it doesn't literary mean what is up in terms of direction or position, if you know English you know what it means :-) 
This is a superfluous comment, but maybe it fills in a little gap for someone....

لا تفوّت فرصة تعلّم لغة جديدة وأنت مرتاح في منزلك. تصفّح مجموعتنا المختارة من مدرّسي اللغات ذوي الخبرة وسجّل في درسك الأول الآن!