The main accepted difference resides in the methodology.
The FDI method also called the direct incorporation is known to be more demanding in terms of documents. For instance, if the shareholders are individuals, in addition to their passport, they will have provide proof of funds for the amount of capital they wish to invest in Vietnam. These documents provided by the banks in the origin country will have to be legalized at the local Vietnamese consulate/embassy then sent to Vietnam for processing the Investment Registration Certificate. This IRC is the “permit to invest” in Vietnam, once obtained, getting the Enterprise Registration Certificate (also known as business license) can be obtained within days.
The M&A method also called the indirect incorporation, is described when an investor enters the Vietnamese market by acquiring a local company. The advantage of this method is mainly that the capital (if it is not higher than a certain amount) must not be contributed by the investor (when the registered business activity does not come with a capital condition). It makes the most sense when services companies are incorporated as these do not need a big amount of capital to start operations. There are several other benefits, for instance if you wish to open a restaurant, that will be discussed in others posts.