ACH(EFTS in EU) in the US is generally free, but has a delay for clearing and has some mechanisms for reversal. This is primarily a digital check, and can be initiated by the receiver in that way.
A wire transfer is nearly immediate by comparison and offers almost no option for reversal. This option does usually have a fee and is generally reserved for large purchase transfers and emergency situations were verification of receipt is required. Such as buying a house. These transfers are processed via Fedwire inside the US and SWIFT out.
The guideline in the EU is that interstate can not cost more than intrastate, so most went to 0.