What is the difference for a company changing 401k company to another 401k company if it is called a transfer or a merger?

I don't understand your question. The term "merger" implies two companies becoming one. If your employer changes firms that administers the 401(k) for their employees they would probably call it a "change of plan adminsitrator" but may call it a transfer of accounts from one firm to another.

First, its not a good idea to piggyback your question on another thread. To avoide confusion I've moved your post to its own thread.

A company changing the plan administrator has no affect on the plan other than changes in the investment options being offered. The plan itself would not change unless they specifically change the provisions of the plan according to the IRS guidelines.