Well in terms of the representation, "kung fu" is just a non-standard romanization, or a romanization of the sound in a different Chinese language. So "kung fu" and "gōng fū" represent the same terms (congou is also sometimes used, which I believe is a transliteration of the term in one of the Min languages, probably the Xiamen dialect, which is the port that a lot of Chinese teas were shipped out of back in the day). This is the same reason we have words in the vernacular which differ from the current standard system (tao vs. dào, oolong vs. wūlóng, tofu vs. dòufǔ, etc.). Some come from older romanization systems like Wade-Giles, and others come from less standardized transliteration.
I am neither a linguist nor a native speaker of Chinese in any way shape or form, but my understanding is that 工夫 is slightly more correct in the context of tea, though you will see both 工夫 and 功夫 used (whereas 功夫 is almost always used, AFAICT, for the martial arts usage). The phonetic sound and the tones are the same in Mandarin, and, I believe, Cantonese (not sure if 工 and 功 sound the same in Chaozhou and Fujian dialect). Both (compound) words also have multiple possible meanings, including some overlapping ones.
Some more detail in this Language Log post
(make sure to read the comments as well as the article itself) as well as here
Just based on a straight Google fight, "功夫茶" (in quotes) seems to have 4,000,000 results vs. 694,000 for "工夫茶". So it seems like the former may be more common in contemporary usage. However, the scholarly publications and books I've seen seem to lean towards the latter.
As best I understand, the meaning has to do with the effort, skill, and attention involved (which, presumably, on some level, is also the root of the use of the term in reference to martial arts), but doesn't imply that tea-making is literally a martial art, as much as some people might like to make that connection.
There is also some speculation on the Wikipedia page
, which expands a bit on the subject of how the term came to be associated with martial arts in Western countries (the Language Log post also spends some time on this subject). Most Chinese folks I know who practice or refer to any kind of martial art would be more likely to say 'wushu', or refer to a specific disciplines, vs. calling it 'gong fu'.
Also, to answer your question, I think that whichever variant of the word you choose, the characters are the same in either simplified or traditional characters (功夫茶, 工夫茶), and I believe 功夫武術 (gongfuwushu) is also the same.
Paging Professor M to the white courtesy phone.