They can quite easily make you redundant from your current job. I assume that is basically what they are doing, but giving you the option of the other job.
This happens often when a corporation is restructuring its legal structure. If employment conditions are the same there is nothing to worry about. Only check that you can keep your corporate years of employment and make sure you don't get a new probation time.
True of course, but in hindsight the same can be said for the current company, since they are suddenly laying off people and changing structure.
You will have time to assess the new situation and decide if and when to leave, this is good. You might have lost a big severance package, but you are keeping your full salary and if you find a better job all of this won't matter anymore.