ExFat is a file system, basically when you first get a new drive you need to decide what file system you want to use. There are various choices. NTFS is standard for PC, you can use FAT32, but that’s got a 4GB file limit. Mac is standard is HFS+, hence the confusion between the 2 systems, but it can be overcome..
A HFS+ Mac can connect, and read and write to an NTFS pc if you connect to it via smb. On mac desktop apple K then type smb://10.0.0.** (mostly likey, it’s your computer or HDD’s IP address, you need to find out what that is.)
Tbh I’m probably over complicating things, you just need to pick the file system and plug it into your computer (I’ve just realised you are just talking about a USB HDD, so plug and play, format it as Exfat when you get it.)