if you are referring to the way they are read, there are more often than not several ways to read kanji; onyomi (音読み) is based on the chinese pronunciation of the character, and kunyomi (訓読み) is the Japanese pronunciation (such as the examples you gave). The character still means the same thing, but its reading is changed depending on how it is used. By themselves, 山 and 元 are read as yama and moto, but in words such as 山地 and 元気, they change to the onyomi readings.
Names are a special case, and sometimes have a special reading called nanori (名乗り), which can be combined with the other types of reading. Names are a subject unto themselves, as they are sometimes difficult even for Japanese people to know how to read or pronounce.
By doing a google search for these terms, you can find more detailed explanations. A good kanji dictionary will tell you all the possible readings for kanji. If you're looking for a free online dictionary, i recommend Jim Breen's WWWJDIC: Jim Breen's Pages Have Moved
I would recommend learning hiragana and katakana before worrying too much about kanji; they're not that tough and they'll make understanding pronunciation keys much easier.
Thousands of chinese characters are used as kanji in Japanese. Most people learn about 3000 throughout the course of their education but there are probably about 6000 that come up with some degree of frequency in Japanese writings. Many Chinese characters do not exist as Kanji, such as the "ni" in "ni hao," and some are used almost exclusively in simplified form, such as 売 (buy), and 国 among many others. Kanji also includes 国字 (kokuji) which are not technically Chinese characters, such as 畑 and 働.