Software safety classification required by the CE (According to IEC 62304) is based on the product type. The classification is 1, 2a, 2b, 3 (major).
The FDA safety classification is called level of concern, and it talks about the potential harm to the patient/user. There is Class I, II, III.
There is a list of questions to ask in order to determine the safety classification, such as “Is the software part of a product with high risk”
The risk management is on system level and is not related to the level of concern