IDE is emulated PATA with legacy Master / Slave relationships.
AHCI is Advanced Host Controller Interface, it's the native host protocol for SATA and is very similar to SCSI. Host Swap / Native Command Queuing / and Port Multipliers are all features that aren't available in IDE. Also this does away with Master / Slave relationships and instead use's HBA / Bus / Target ID (port ID) to identify devices.
RAID is just passing control of the AHCI interrupt to the storage controller's BIOS. The storage controller will then abstract an AHCI storage device that represents a RAID group.
There are two differences, the first being that you will need to prepare "storage driver installation" media for AHCI / RAID modes. This is the driver that Windows will use to talk to the storage controller. This may be uncomfortable for home users but has standard for enterprise SCSI controllers for two decades. Using "IDE" mode will bypass this requirement, then you are using the built in Windows legacy IDE drivers, which is not exactly an idea situation. The second is that there will be a severe performance penalty associated with running in IDE mode vs AHCI/SATA. This penality comes from two directions, first being that windows legacy IDE drivers are not optimized for your storage controller, and the second being that IDE doesn't understand NCQ and out of sequence read / writes. IDE use's a FIFO buffer that is non optimal when your multitasking.