2013 MacBook Pro hard drive typically partitioned

The partitioning format of the hdd or ssd depends on the version of the macOS that is currently installed.

The 2013 Mac probably shipped with Mac OS X 10.8 or 10.9. Those would have had a drive formatted with HFS+ (Mac OS Extended) with a single partition encompassing the entire capacity of the drive.

Versions of macOS since Mojave use a more advanced file system - APFS. This system creates a container on the drive, and within that container are created APFS volumes (partitions). A standard MacOS Catalina installation would have two visible APFS volumes named "Macintosh HD" and "Macintosh HD - Data". They would appear as to have the same size, equivalent to the 500 GB drive size.

Your drive, with equal partitions of 250 GB, apparently was manually partitioned. It could be either the older HFS+ format or the newer APFS. You can inspect the drive format in the Disk Utility application. If you wish additional help, it would be useful to post screenshots of what you see in Disk Utility.

What macOS version is currently installed?

You've chosen to "learn" the Mac with an obsolete, twelve year old computer. Things have changed and that Mac is not equipped to provide productive service in a graceful way today. It cannot run any currently supported macOS. MacOS Catalina 10.15 is woefully outdated and unsupported. It is six generations behind the current OS Sequoia.

10.8 is the shipped in the box version, and uses HFS+ Extended format. it does NOT support modern encryption, so using the regular web with less than 10.11 El Capitan will be 'challenging' (read, impossible).

if you want all your space for use with MacOS, you will need to ERASE the drive:

boot into Recovery, where macOS Base System is expanded from the Mac's ROM and used to support included Utilities like Installer, Disk Utility, and Terminal. Disk Utility can Erase the drive, but in 10.8 Recovery, can only provide HFS+ Extended (APFS was first introduced in 10.13 High Sierra)

Once you have set up a MacOS with an Apple-ID, later versions of MacOS will become available, and Readers can help you install them.

when you have upgraded to MacOS 10.13 High Sierra, a container disk will be added, which changes macOS HFS+ Extended into simple APFS

If/When you upgrade to 10.15 Catalina, the full APFS format including a separate crypto-locked System drive will be provided on installation.

it is also conceivable that the drive was deliberately partitioned for a Windows installation on half the space.

In general, it is superior to completely ERASE the entire Physical DEVICE and install a new instance of MacOS from scratch, of the "shipped in the box" version, then upgrade to the version you desire. This would remove the partitioning information and start fresh.

Good advice, but I suggest a refinement:

Rather than make a close of what you have, which will never work on the internet, you may prefer to make a Bootable USB stick (8 GB or larger required) of MacOS 10.11 El Capitan, the oldest version that CAN get on the internet.

Faithfully follow the steps in this article under bootable USB stick after downloading 10.11 Eli Capitan and opening the resulting .mdg file, and opening the .pkg file inside, which runs an Installer that places a macOS 10.11 El Capitan Installer in your /Applications folder.

How to download and install macOS - Apple Support

PA-WOODCHUCK wrote:

I been a windows user forever but venturing into MAC. Here's what I know...

MAC OS-X 10.8.5 HFS+

I have a disk1 OS-X base system which I presume is for recovery

Yes, the Base System is for recovery only.

That said how do I ease everything and return to "out of box" including correct partitioning?

Ideally, before you do anything, I strongly suggest you make a cloned copy of the current working system to an external USB drive. It may very well come in handy if you find it difficult to re-download macOS for some reason. That happens a lot! You can use an older version of SuperDuper! to do that. Download the version specific for Mac OS X 10.8 Mountain Lion.

If you can coax the Mac to boot into recovery using the key combo Option-Command-R (⌥⌘R), you may be offered macOS Catalina to be reinstalled on the computer. This would be the ideal OS for that Mac. If you can get Catalina without having to download and reinstall earlier OSs, that would save much headache.

❝ If you used Option-Command-R to start up from Internet Recovery, you might get the latest macOS that is compatible with your Mac.❞ - How to reinstall macOS - Apple Support

D.I. still researching which model to purchase down the road.

Maybe you will find something helpful here: Mac - Which Mac is best for me? - Apple

one more thing about those cryptic terminal commands for making the bootable USB-sticks:

When erasing your USB stick, be sure to name it exactly MyVolume, so that you do not have to change the scripts in the slightest.

Then copy the ENTIRE terminal command-line from the article (which is wider than the page) and PASTE at the Terminal prompt and press return.

👍🏽