Categories all messed up after import to new host

I am moving my blog site https://lessbeatenpaths.com to a new host because my current host is too slow and site edits keep getting bogged down. The site is using the default Twenty Fourteen Theme. The new site is up at https://lessbeatenpaths.hostguardian.com and I plan to redirect the DNS as soon as it is working properly.

When I did an Export and then an Import, including export of .xml and .sql, the Post Categories on the NEW HOST were all messed up and, in fact, some of them should have been Tags and not Categories. I have over 100 posts and am concerned about getting these Categories fixed. I have looked in the PhpMyAdmin thinking there was a way to do it there, but I could not find it.

If you look at the most recent post on both sites, you will see the categories listed above the Post Name and you will see the differences immediately.

I also manually moved the categories.php and tags.php file over from the old server to the new server, but that still didn’t fix anything.

Is there any “easy” way to get the proper categories onto the NEW HOST site without having to rebuild and recheck all of the content?

Any suggestions and/or advice would be greatly appreciated as I have four more sites to move from the current host to my new one.