שבי means "captives" referring to the people themselves.
שִּׁבְיָה means "captivity" referring to the state of being imprisoned.
Compare the use of the term שִּׁבְיָה in the Mon. - Thurs. davening just before returning the Torah "Acheinu kol bet yisrae'l..." the term שִּׁבְיָה is used, there because it means the state of captivity.
The use of the 2nd term makes sense, and the reason for the switching in terms is that in the 1st verse, the Torah talks about the general results of the war, in other words, it is explaining the circumstance. You went to war, G-d made you successful, and you took all its captives שבי .
Now, you have all these captives. You see a beautiful woman. You want her as your wife. The woman has emotions about her being imprisoned, and the Torah is speaking about her state of captivity and what that does to her and how you should treat her feelings; not so much of her "physical" status of being a captive. Hence, the use of the term שִּׁבְיָה, since the Torah is instructing you how to deal with her feelings of captivity - the emotions and her captivity status, not the fact that she is a "captive". A careful analysis of the following verses indicates that once you intend to take her as your wife, she is no longer like the rest of the "captives", but, since she has to shave her head and mourn her parents (who may still be alive, actually), she is still in the state of "captivity" until she officially becomes your wife a month later.
Another way to view things:
The 1st verse means - "You shall take its (the enemy's) CAPTIVES"
The 2nd verse means - "You shall see a woman in captivity" vs. having said (if it had used the word שבי in the 2nd verse,) "You shall see a woman among the captives".
So, there is a BIG difference in meaning.
The Torah (G-d) chooses (His) its words very carefully...