Without additional tools? That's a tough one. The arp -a command only show's you what already exists in that devices cache. Which, if the device you're trying to find has never communicated with that device you're on, that device wouldn't be in it's cache. That's why only devices you have sent a PING request to are in your arp cache. To find IP Addresses associated with MAC addresses, you need a scanning/discovery tool like Angry IP Scanner (https://angryip.org/) or Advanced IP Scanner (https://www.advanced-ip-scanner.com/). Those tools are free, don't need to be installed to use, and will scan the network for any devices then show their MAC Address, IP Address, along with any associated data like Manufacturer, Hostname, etc.
Otherwise, the long way is to lookup the OUI. The first half of every MAC Address is manufacturer specific. Enter the MAC Address (or MAC OUI) into any MAC Lookup website (just google it, they're everywhere) and it'll tell you the manufacturer associated with that MAC Address. From there you should be able to guess what device that it. You can also look at your router's MAC Table, ARP Table, or Routing Table. But the easiest way is to just run a tool like Angry IP Scanner or Advanced IP Scanner. They're free, portable, and will give you all the info you're looking for.