These two are known to be processes of consolidation. The merger is a process that will combine two companies so that one company that is struggling can be absorbed by the thriving company. This will allow the failing company to be saved and the thriving company to become stronger.
Amalgamation means that there are different companies that will also be combined together, but instead of keeping their separate company names like in mergers, the companies will form a completely different company and will dissolve their past company names. This can be used when two companies are working towards the same goal, and they feel that they can combine their businesses for their own gains.