Connecting two seperate objects with vertices

So I have 2 objects I want to connect using vertices but i tried selecting both then edit but it only lets me access the vertices on one or the other thus not able to connect them. And if i do crtl j they form into a single object . How can i merge them but keep them as seperate objects?

Hi Richard
Thx that should be just what i need but unfortunately it did not work:(.The issue is with a long tail cloak I want the back to be effected by a cloth modifier but the front to not. I am importing my model to Unity and even though i stitched all the vertices back together it treated them the same as 2 objects. The screenshot below will show the issue I am having with 2 object and single object mode. Not sure how to resolve this now.

This is how it looks after using the multiedit tool which is exactly the same result as you get with 2 seperate meshes.

And when as a single object the entire coat is effected and gets pulled through the body.