Tell me how to explain to someone the difference of a merger and a Buyout?

Hers how I tried to explain it:

Merger with and other CO mean that they are usually in the same industry and want to profit off the potential synergy of joining the 2 organisation even though 1 has to actually buy the other.

A buyout is just a firm buying an organisation and usually they will not manage it long term. There main objective is to buy an organisation and usually divide it up to more manageable companies and sell them for more then they paid for the whole organisation.

So bottom line a merger is a buyout but usually the buyer intends to continue the business and wants to profit off the possible sayings coming from redundancies while a buyout is a reselling of the organisation in more manageable pieces.

Am I right?