Pretty much what everyone above said. By the economics/business textbook definition:
A merger is when one company, the merging partner, issues an ownership interest in that company to the owners of the second company, the merged partner. The first company continues to exist under its original articles of incorporation, and the second becomes a wholly owned property of the first, and may be dissolved or kept as a subsidiary as the first company, now with the additional ownership of the owners of the second, wishes. That's what Delta and Northwest did. Delta issued Delta stock to the shareholders of Northwest. The former owners of Northwest are now among the owners of Delta. Delta continues to exist under its original articles of incorporation. Northwest is... I'm not sure if Delta dissolved it, or continues to keep it in their corporate structure as a subsidiary. It's also what America West and US Airways did, but with a twist. HP
was the merging partner and US was the merged partner, but at the same time, HP
changed their name to US Airways, which they could do since they owned the name as part of the merger. Nonetheless, the US that exists today exists under the America West corporate charter, and former US shareholders are now shareholders in the company.
A consolidation is when the shareholders of two or more companies create a new company under new articles of incorporation and a new corporate charter, and transfer the assets and liabilities of both (or all) previous companies to the new one. The new, consolidated company now exists, and the older ones are either dissolved or kept as subsidiaries of the new one. That's pretty rare these days, because it's lawyer-intensive, and therefore more expensive.
An acquisition, colloquially called a buy-out, is when one company offers cash or something of value other than an ownership interest in the company for the assets and liabilities of another company. The first company continues to exist. The second company is dissolved or becomes a subsidiary. The previous owners of the second company have no ownership in the remaining company. They are literally bought out.
An asset acquisition is when one company offers cash or something of value other than an ownership interest for all or some of the assets of a second company. Both companies continue to exist, but the assets transfered now belong solely to the first company. This is what AA
did with TW
was being liquidated, and the value of the assets were used to pay off the remaining debtors.
There are other permutations, too, but those are the ones that happen most with airlines.
Again, these are economics textbook definitions. In common speech, the distinctions are not always made.