External Hard drive for Mac?

The ones that a Mac ready just means they have been formatted as Fat32. You can use any external hard drive and format it yourself as Fat32 and it will work perfectly with Time Machine on your Mac. 

You can use any external USB, eSATA hard drive in your Mac as it will format it to work to specs!

Probably just costs more with the word "Apple" on it

By a cheap USB stick.

if that works reliably for a period of use.

that would indicate that an "external hard drive would be compatible".

As far as i know you are not meant to format or partition any USB drive

No, there are no specific software for external hard drive for mac. it's just a different OS not a differne t world that you enter after using mac. So things remain same.

Any USB external HD can be used with the Mac. 

You can format it using disk utility to the Mac format or a common windows format of FAT32.

Macs can also mount and read and write a NTFS (newer windows format) with a small helper program.

External HD unless specifically labeled Mac would come with NTFS or FAT 32.  

If you are going to go from Mac to Windows or back use FAT32. 

FAT32 is the "Type O" of disk formats because in general every computer knows how to read and write to it. That makes it Mac compatible but not "for Mac". If you are not likely to move the drive between Mac, PC, or Linux you can convert it to the best format your system uses.

No, mac can use ExFat but they now use Mac OS extended or the new APFS.  If you don't move files to a PC, then you are better off with an Apple Filesystem.

If the interface works (Tbolt/USB) then the only difference is that the disk is preformatted so it works off the shelf. Some come with optional software for cloud backup or local backup.  If you don't need that, then it makes no difference.

Mac use their own format for internal drives; APFS or HFS+, if I remember correctly.

FAT / ExFAT are used for USB drives to allow compatibility between systems, but each system (Windows / Mac / Linux) has its own native filesystem types for internal drives, that give better performance or better security etc.

A natively formatted drive will work better, but not be compatible with other system types unless you add extra software to the other systems to allow them to read the "foreign" filesystems.

You should be able to repartition and reformat any drive to work with any system.

The only other consideration is that Macs support different connection types as well, eg. Thunderbolt rather than USB; in older machines they used different connector types - but now USBC-C and Thunderbolt use the same connector.