Acquisition Method and Purchase Method are both accounting process which is similar in several instances, but still have some differences between them. One of the major things that distinguished between these two terms is that the purchase method has a price allocation mode (that is a more discretionary purchase), while the acquisition method posses a recognition mode that is more market-driven.
In the purchase method, the business combinations do not reflect at full fair value, while it is on the contrary for the acquisition method. Another thing that will most likely not be seen in a purchase method is the non-controlling contingencies and interests but is included in the acquisition method.
The acquisition method happened to be the standard form of accounting that first came into force. The purchase method, which is used for an acquisition or merger, sometimes came later. The financial statements in the acquisition method are seen to have more relevance and transparency.