Every hard disk drive (HDD) and every solid state drive (SSD) on this planet can be used either as internal drive or external drive.
Some external drives come in enclosure/HDD case (or however you wanna call it) so you will need to take it out of it in order to be able to properly connect it to the motherboard.
And yes...if you have the cables then you can connect the drive to the motherboard just fine.
NOTE: On some old motherboards you might need to use the PATA to SATA converter...for example if you want to connect the SATA drive to a motherboard which only supports PATA.
But no matter what the conditions are...it is ALWAYS possible to connect ANY drive to ANY motherboard.
And wether the converters are needed or not...that really depends on your drive and the motherboard.
Here is my simple case.I have a 15 years old PC and I wanted to use internal SATA drive.However my motherboard supports PATA only so I used the following converter chip to accomplish my task:
This is the EXACT chip I am using!
And it's cheap as hell and ALSO it supports conversions from PATA to SATA and from SATA back to PATA and it can be used to convert any PATA or SATA HDD drive,any SATA SSD drive,any PATA or SATA CD/DVD-ROM drive on various ways such as:
2.5 or 3.5 PATA HDD ---> 2.5 or 3.5 SATA HDD
(Yes 2.5 HDD drive CAN be used as an internal drive in desktop computers if you want).
or
PATA CD/DVD-ROM drive ---> SATA CD/DVD-ROM drive
And so on...there are no limitations.
Oh and...if someone tells you that these converters never work,don't listen to them lol.Because they work perfectly fine if you do things right.
Cheers!