Traditionally the difference is very distinct. A data logger is an electronic device that records sensor data over time. Generally they are small, battery powered, equipped with a microprocessor, internal memory for data storage, and sensors. Data loggers are typically left unattended to measure and record information for the duration of the monitoring period.
An RTU however, does much more. It can not only collect data but also interface objects in the physical world to a distributed control system or SCADA (supervisory control and data acquisition) system by transmitting telemetry data from them and by using messages from the master to control the connected objects.
More recently the lines have become more blurred as data loggers have become 'more connected' able to transmit telemetry data to control systems. So the the main distinctions have become about how sophisticated the devices are in their functions of collecting and transmitting telemetry data (i.e. whether they can send alarms etc) and whether they can control physical objects, RTU's can, Data Loggers cannot.