What are the differences between throughput and transmission rate?

The differences between throughput and transmission rate are clarified below.

Transmission rate of a terminal or a medium is defined as number of bits that it can transmit per second. It is associated with an individual component of a communication system. It describe the potential of the communicating terminal or medium.
For example

Transmission rate of fast ethetnet LAN is 100 Mbps.
Transmission rate of dial-up telephone is 56 Kbps.
Transmission rate of dedicated link between two devices.
Transmission rate of a source communicating terminal.
Transmission rate of a destination communicating terminal.

Throughput is defined as the actual number of bits that can be transmitted in a second between two communicating terminals. Throughput is a collective approach of describing number of bits being transmitted per second between two communicating terminals.

For a single link :-

If source and destination terminal are connected by a single link then transmission rate is equal to throughput.
i.e. Transmission rate = Throughput.

For multiple links :-

If source and destination terminal are connected by multiple links then throughput is equal to the transmission rate of the link which has minimum value.
i.e. Throughput = Minimum {TR _L1, TR_L2, TR_L3, TR_L4 ............ TR_Ln}
Where,
TR_L1 = Transmission rate of link 1.
TR_L2 = Transmission rate of link 2.
TR_L3 = Transmission rate of link 3.
TR_L4 = Transmission rate of link 4.
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TR_Ln = Transmission rate of link n.

Numerically "throughput" is equal to or less than transmission rate.