Jim, it is hard to say whether you need to delete the other database references from wp-config.php or from your database server without taking a look at the site’s backend, the files in wp-content and database(s).
You can disable Jetpack by using cPanel (or FTP) to navigate to /wp-content/plugins/ and then to rename the ‘jetpack’ directory by adding an ‘x’ in front of the name.
Just a quick explanation of what those backup files are and of how WordPress functions:
I don’t know whether you are familiar with database programs like MS Access or LibreOffice Base. If you are, keep them in mind as I go through this explanation, otherwise bare with me and (I) hope you understand the general gist.
Think of WordPress as being like a database application. It has two graphical ends: the admin area and the public area. Only those given login access to the admin area ever get to see the admin area. Anyone can view the public part of the website (unless blocked or access is restricted).
We use the admin area to create content. We use the public part of the site – the front of the site that most people see in their web browsers – to view the content that site admins (editors & authors etc…) create.
Here is how this (WordPress) relates to MS Access/LibreOffice Base and other database programs: Think of the admin area as being the place where you perform data entry tasks and organise how that data is viewed by your site’s visitors. You have a form (where you create posts), you add text to that form and upload images (or other media) that is to be shown alongside the text.
WordPress adds HTML markup to the content you create. This is the purpose of the visual editor (TinyMCE): you add text then click buttons to make the text pretty; ditto for images.
So, how is all this text stored and how are all the media files stored?
The text and HTML markup is stored in a MySQL database (usually MySQL). This database is stored within your hosting space in a ‘database server’
The media files are stored in your hosting space on your web server. These files are not stored in your database server.
The database stores all the text, the HTML and – by virtue of the HTML – stores references to where your media files are stored on your web server.
The media files are stored in the directory ‘/wp-content/uploads/’, the plugins are stored in ‘/wp-content/plugins/’ and your theme files are stored in ‘/wp-content/themes/’. The common directory for your non core WordPress files is ‘/wp-content/’.
How does this relate to your question?
You have two backup files: one is an SQL file, one file is a zip file that contains all your uploaded media, plugin and theme files (this is the ‘non text’ part of your creative content).
To answer your question:
The file to import into phpMyAdmin is the SQL (database) file. This contains your text. The other file contains the media uploads. The media files should still be on your web server. I suspect your original database is also still on your web server.