Are those synonyms? Is one more acceptable in a certain dialect than the other?
I checked their definition on The Free Dictionary but it's still not clear to me.
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Technique and technic are synonyms (as shown on Merriam-Webster's entry for technic).
Note that technique is by far more used than technic. Compare the number of matches found for the two words:
Corpus of Contemporary American English (COCA) technique = 13383 technic = 18 British National Corpus (BNC) technique = 4601 technic = 9 Google technique = 271M technic = 14M
According to the data from Google Ngram Viewer shown below, technic was more commonly used between 1900 and 1970 than it is today. As for technique, usage increased since the early 1900's until now, except in the past two decades or so, in which for some reason (?) the number of occurrences decreased in comparison to other general words.