Daily I see peoples even specialists in communication do mistakes about the three mentioned terms:
Bandwidth: The unit of it is
Hz, so it is mathematically is: High_Used_Frequency - Low_Used_Frequency. So, when we measure bandwidth in bps, i.e we do mistake. Besides, some guys working in Network field, totally they treat with the bandwidth as Data rate. So, bandwidth is the difference between high and low frequency. For example, bandwidth of a channel in FM is 0.2MHz, for a carrier is WCDMA is 5MHz.
Data Rate: The unit is
bps, so we can say that the data rate of the channel is the maximum ability of the channel that can transmit bits in a second. In the normal case, we can say that if we have 5MHz bandwidth, then the channel capacity (or data rate) is 5Mbps, but also it can be that the bandwidth is 5MHz but the data rate is 10Mbps, or 2.5Mbps, this is depends on the modulation type and some other technics.
Throughput: This term is used in many different systems, shortly, and clearly we can define it as: the real data that we receive. For example, the Bandwidth=5MHz, channel capacity(data rate)=10Mbps,but what we receive exactly is 6Mpbs due to any reason, so the throughput is 6Mbps... Hope I gave you an idea...