All three are for the same word ( work, do) and the 1st and last are from the same origion: 爲. This is the primal form in the earliest ever Chinese writing today we've found.: carapace-bone-scrip ( carvened or scribed in bones or tortoise shells, actually). In its original figure the top 4 strokes, which makes the word 爪，stands for man's hand, and the lower part is an image of an elephant. The entire figure makes the sense of man leading an elephant to work ( plough, draw carts, etc; In old ages elephants were widely distributed in Asia and were commonly used as animal power in ancient China). ;) The second produced form is 為. Limited by reference material I cannot precisely point out when it had come into being. It is simply a casual or reduced writing for 爲. And for the convenience in writing it has been more used than 爲, but, as you've mentioned, the two are absolutely exchangable without making any diffence in meaning or style (except for archaism, but then again, very few people today know which ever of the two had come earlier). As for 为，it's a simplified form for 爲 and 為. This form is from the traditional cursive writing for the latter two. It is included in The Chinese Character Simplification Scheme, which was legitimated and issued by the P.R. China government in 1950s and 1960s; whereas the simplification of Chinese characters have been proceeding all the times, 为 as a simplified form for 爲 and 為 has a very long history in people's daily handwriting and the above Simplification Scheme therefore included and legitimated it. Today in mainland China and Singapore (and lawfully in documents about affairs concerning other countries and the P.R. China or in the UN), simplified characters are commonly used and in Chinese Taiwan and Japan traditional characters are more used.

Actually the three characters 为, 爲, 為 are same, 为 is simplified Chinese, usually used in China mainland. 爲 and 為 are traditional Chinese, usually used in HK and Taiwan. Chinese mainland government simplify these two traditional characters to 为 in 1950's because of the complicated writing.

爲 is more traditional than 為 while 為 is easier to write than 爲. They are the same.

为在作介词、连词、助词和语气词时作爲，其它情况下两种写法都可以。不过两种写法的字的原形是一样的，人手执象。