1)
What is "Ta'avasi"?
1.
Rashi: My needs.
2.
Radak: My desire to live (recover) from my illness. Since he mentioned Sha'agas of his heart, he mentioned Ta'avah, which is in the heart. Whether or not I roar, You know what is in my heart!
3.
Radak citing Ibn Ezra: Ta'avasi is Negdecha - only You can make me live; the doctors cannot.
4.
Sha'arei Teshuvah (1:4): My desire is only for Your Avodah.
5.
Malbim: It is the heart's desire for the future.
2)
What is "Anchasi"?
1.
Radak: It is sighing over his illness.
2.
Sha'arei Teshuvah (1:4): My sighing is only over my sins and my shortcomings in Your Avodah.
3.
Malbim: It is sighing over the past. Even though I cannot speak, You know thoughts.