I am very confused about when to use bandwidth as bit rate and where not. Are these terms one and the same?
As hinted by Mr Duval, the term "bandwidth" has been adopted by networking engineers to mean something similar to "transfer rate" (just as "wideband" in networking tends to mean "high speed"). You've tagged your question "digital communications", though, where the term is very precisely defined.
Bit is the unit of information in information theory. Intuitively, a bit is the information conveyed by the answer to a yes/no question, where each answer is equally likely.
In communications we want to transfer information from a transmitter (information source) to a receiver (information sink). The information transfer rate is measured in bits per second. Informally, you can think of this as the number of zeros and ones that a system can transmit per second.
However, it turns out that information is transmitted and received using physical, analog signals (voltages or electromagnetic (radio) radiation). These signals pass through a physical medium, called a "channel", that acts like a filter: only certain frequencies make it from the channel input to its output. So, the channel is said to have a bandwidth, just like any filter.
One of the main jobs of communications engineers is to transfer information as fast and reliably as possible over a channel of given bandwidth. Basically, the problem is how to design a physical signal that:
- Fits over the channel bandwidth
- Conveys bits at a high rate
- Does so reliably (with few bit errors at the receiver)
- Does so at feasible complexity at both transmitter and receiver.
The design of such signals is, in a broad sense, covered by the term "modulation".
I hope this is clear -- please comment if you need clarification.
In communications engineering, bandwidth is the measure of the width of a range of frequencies, measured in Hertz.
Rate is the number of transmitted bits per time unit, usually seconds, so it's measured in bit/second. Equivalently, it can be given in symbols/time unit.
The rate is proportional to the system bandwidth. The Shannon Capacity is one theoretical way to see this relation, as it provides the maximum number of bits transmitted for a given system bandwidth in the presence of noise.
Also, in the specifications for each communication's standard, you can find the exact relation between system bandwidth and achievable rate (which is smaller than the Shannon Capacity), and these depends on other parameters such as type of channel and modulation order, but the two magnitudes are still proportional.