They call it a merger, but in fact AMD did acquire (e.g. bought) ATI. The only real differences between a merger and acquisition are the way the deal was worked out and how it is pitched to shareholders (or the public).BTW, AMD merged with ATI, not bought, so wouldn't the combined ATI-AMD have the combined assets of both companies, including the majority of the stock issued and money paid to acquire ATI?
If Company A acquires Company B in a process of mutual cooperation where Company A essentially gives Company B as much say in how things are going to be done (or whether it will be done at all), its called a merger ('equals').
If Company A isn't really seeking approval from Company B, or one company is substantially larger than the other, its called an acquisition. However, the acquiring company often will allow Company B to call the deal a 'merger' purely in the interest of public or shareholder relations.
In both cases, one company is acquiring the other and the acquired company ceases to exist as a legal entity. Whether they decide that the name of the new company will be 'Company A', or 'A + B' (e.g. DaimlerChrysler or ExxonMobile), or an entirely new name, doesn't change the fact that one was acquired by the other.