Bandwidth
Bandwidth consists of a characteristic related to the links of network topology. This characteristic indicates the frequency width supported by a particular link in a network. So, we employ the Hertz (Hz) unit to express bandwidth. It directly influences the data rate and throughput in a networked system. Here, we talk about the Physical Layer (OSI Model). Bandwidth defines physical limits that can not be transposed.
Data Rate
The data rate refers to the maximum capacity of a link channel to transmit data in a period. Usually, we use bits as data and seconds to indicate the period. Thus, the traditional metric for measuring the data rate of a system is bits per second (bps).
The data rate is a characteristic defined between the data link and the physical layer, considering the OSI model.
Throughput
A generic term employed in multiple cases in computing and networking. In our scenario, we can see throughput as the real data we receive/send in a certain period. The capacity to transmit real data (the throughput) is naturally smaller than the data rate since we use part of the data rate to send this extra data (typically presented as a set of headers encapsulating the real data).