The main dictionary definition of "conservative" is "holding to traditional attitudes and values and cautious about change or innovation, typically in relation to politics or religion." In European and Latin American history, "conservative" usually referred to supporters of the Church (and sometimes landed gentry), which was opposed to business interests. A strong strain of paternalism runs through the history of the European/Latin brand of conservatives. Pro-business advocates were (and still are) called "liberals" in Europe (if you read the Economist, a liberal is pro-business and has nothing to do with "traditional values"). In America, due to the vagaries of political coalitions and animosities, being pro-business slowly evolved to be labeled "conservative", partly due to shared antagonism with traditional conservatives towards the State. It is true that traditionalists and the pro-business want limited government, but their reasons are different (for the former, it is more to protect sacred values; for the latter, it is more to be free to build and creatively destroy - hardly a "conservative" impulse). But does overlap in some concerns warrant a common label?
In America, pro-business types and social conservatives have formed an alliance. Sometimes common cause and common adversaries lead members of different groups to adopt at least some of the views of one’s allies. But that is not the same as whether these diverse views go together “naturally”. Separate from its historical association with conservatism in America, is being pro-business inherently conservative? In what sense?