What cable do I need to transfer data from old MacBook Pro to new one

I have a very old MacBook Pro (one with a DVD drive in it). I just bought a brand new MacBook Pro. I want to migrate the data on my old computer to my new computer. I can't find a cord in my house that will connect the two.

Initially I did a backup of my old computer to my external harddrive and connected the two with a regular cable I had. I started the new computer and during the set-up it acknowledged the external harddrive and seemed to be transferring. However when the set up was over there was no info on the new computer.

I have a FW800 cable that can connect my external hard drive to my old computer but the new computer does not have a port to match.

It mentions something about a Thunderbolt. Where do I get a Thunderbolt cable that has the different ends that will fit each device?

This is the old MacBook Pro

This is the external hard drive

This is the new MacBook Pro