Welcome to A.S.!
The holes in the drive links were a feature of some Oregon and STIHL brand chains to help 'carry' oil around the bar, but have been copied by some other manufacturers. Some STIHL chains had grooves stamped into the drive links to help direct the oil to the rivets (also copied by others). These, and other features may help with chain oiling, but flat drive links will work too, if using the right size chain for your saw.
The key dimensional features of a chain are the
pitch,
gauge, and
drive link count. If those are correct, a chain by any manufacturer will fit your saw. Here is one explanation of those terms:
https://www.baileysonline.com/pub/media/baileys/pdf/saw-chain-101.pdf
Sometimes, people will swap out a related component on a saw, such as a bar or drive sprocket, requiring a different chain. Since it sounds like you got your saw used, it may not have the original components supplied by the manufacturer, and you must match what you have (not just look up the saw in a fit guide). Many chains and bars have this information stamped on them, but it often wears off, and different companies use totally different marking systems.
If you post clear photos of your chain that worked, we might be able to help you. Otherwise, take the saw to a
servicing saw dealer and ask what you need.
Philbert