IDE/PATA and AHCI/SATA are the technologies used to connect the internal hard-drive to the computer's brain or CPU and RAM memory on the motherboard, similar to USB 2.0/USB 3.0 and USB-C ports.
....... In general, IDE/PATA is a very old technology that was commonly used in internal hard-drives(= HDD) of less than 250GB in size, eg 40GB, 80GB, 120GB and 160GB. AHCI/SATA is less old technology that is commonly used in internal HDD of 250GB, 500GB and 1TB.
NVMe technology for internal SSD is more modern. SSD can be SATA III or NVMe.
The more modern technology gives faster data transfer speed from the hard-drive to the CPU and RAM.