While black tea is perhaps more popular in the West than green tea, it is not a Western product; it's as Chinese as the rest.
Strictly speaking, お茶、おちゃ, is any tea. Green tea is the most commonly consumed and thus it is generally synonymous, much in the same way that in the West "tea" usually just means black tea. お or 御 is honorific.
- 白茶、はくちゃ, is white tea.
- 緑茶、りょくちゃ, is green tea.
- 紅茶、こうちゃ, is what we call black tea, due the the color of the leaves. 紅 however, is red, after the color of the brewed tea. Yes, there are several kanji for "red". What we sometimes call red tea, or rooibos, is ルイボス茶.
- 黒茶、こくちゃ, literally "black tea", is a class of teas such as Pu'er, whose leaves are fermented. Fermented tea, or dark tea. Not to be confused with what we call kombucha, or 緑茶/紅茶キノコ (mushroom), tea fermented after brewing, which itself should not confused with 昆布茶、こんぶちゃ, or tea actually made with kombu, or kelp, and is not fermented.
There are others still, such as 抹茶、まっちゃ, fine powdered green tea, 黄茶、きちゃ, yellow tea, 花茶、はなちゃ, flower tea, in which dried flowers are wrapped in tea leaves and "bloom" when steeped, which should not be confused with herbal teas, or tisanes, ハーブティー, "herb tea", 麦茶、むぎちゃ, barley tea, which contains no actual tea, and more.
Tea is complicated.
I see someone else knows a bit about tea. ^_^
Here's a short article on "What IS Tea?" - http://www.brigidsflame.com/feymorgaina/blog/?p=126
Arsuru gave a detailed explanation, but the short of it is that tea in general is "お茶" (I have never heard it used as just "ちゃ"). 紅茶 (こうちゃ) is specifically 'black tea'. Green tea is 緑茶 (りょくちゃ) but is so popular in Japan that it is likely that it will be assumed if you ask for お茶 it is by default green tea.
Tea cultivation originated in China, and cha is originally a Chinese word. Words for "tea" in most languages around the world ultimately derive from words in one Chinese language or other, either cha as in Mandarin and Cantonese, or te as in the Southern Min spoken in Amoy, from where Dutch merchants brought tea to Europe. So it's not surprising that your language and Japanese have similar words for tea.