Transfer a WP Website from one URL to AnotherURL

Hello,

I use Bluehost to host both websites.
I am using a test website for a rework
of my old website. I am just about ready to
transfer the new website to the original URL.

Are there some tips about transfering within
the same hosting company. Will the images in
my new site transfer and be read correctly
even though the URL’s contain the test site name?
Or will I have to change the image links?

I don’t think the process is difficult, but
all suggestions in making the transfer
seamless will be appreciated.

Thanks, Jeff