The classification of a device is determined by the risk of the device. If the device in question for classification has a higher risk, it is likely to have a higher classification. However, many device classifications differ between the EU and US. For example, the device class for the urinary catheter is not the same in both areas. A urinary catheter is placed in the bladder through the urethra so a patient will be able to release their urine easily. In the EU, the urinary catheter is classified as a Class 1 device if used for transient use. In the US, however, the urinary catheter is classified as a Class 2 device. The higher classification in the US shows that there is a higher risk considered in the US for the device.

http://ec.europa.eu/consumers/sectors/medical-devices/files/meddev/2_4_1_rev_9_classification_en.pdf

https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfPCD/classification.cfm?ID=1676