Some of these terms are used differently by different people, but below is what is generally accepted.
Bandwidth is the number of bits per second that a link can send or receive, including all flows. For example, the bandwidth of a 100 Mbps connections is 100 Mbps, but that doesn't mean it is always sending or receiving 100 Mbps, but that is the maximum possible on that link. Unlike what many people mean by bandwidth, it does not mean data usage. I see people say that they have a bandwidth limitation (every link does), and they have used all their bandwidth for the month. This is an incorrect use of the term. What they mean to say is that they have a data usage limitation, and they have used it up for the month.
Throughput is the amount of data during a time period that a flow (process to process) can send or receive. This includes all the host overhead, and contention on the link (multiple flows on a link will each use some percentage of the bandwidth, reducing the throughput of each).
Bit rate is closer to bandwidth, but it is often per host, or source to destination devices. You may have a bit rate of 100 Mbps from a host to a switch, but the bit rate from a host to a host is less. This usually includes multiple flows.
Your question is pretty confusing, and it is somewhat misleading, but I will try to clarify.
The capacity to which you refer is called the bandwidth, and it is measured in bps (bits per second). For example, 100 Mbps. The speed of transfer on a cable is fixed and limited by physics (the speed of light in the medium of the cable), and it it relatively the same for all your cables. For example, the speed of light in copper cable is about two-thirds the speed of light in a vacuum. The bandwidth is more a function of the device interfaces than it is of the cable.
There are cable standards set by ANSI/TIA/EIA and ISO/IEC. To facilitate the bandwidth of the device interfaces, the cable must meet some parameters. This can get very technical and complicated, which is why the standards bodies have created various cable standards. For example, ANSI/TIA/EIA has categories for copper cabling, and ISO/IEC has cable classes. The various standards define parameters like Insertion Loss, NEXT, FEXT, Return Loss, Propagation Delay, Skew, etc. Depending on the particular set of parameters a cable has, the cable is rated for a maximum frequency it can transmit, e.g. 100 MHz for Category-5e. How the interfaces encode and signal on the cable determines the bandwidth, but a cable must meet the requirements of the interfaces in order to function at the bandwidth of the interfaces.
A big part of whether or not the cable can function correctly at a particular bandwidth is determined by the cable installation. There are standards for this too. For example, ANSI/TIA/EIA 568, Commercial Building Telecommunications Cabling Standard. Poorly installed cable will not function correctly. All components of a cable path (cabling connectors, etc.) must be rated the same, installed properly, and tested with expensive equipment to validate that they perform correctly.
An example of the cable bandwidth would be Category-5e cable. If it is properly installed, the cable can work at 10BASE-T (10 Mbps ethernet), 100BASE-TX (100 Mbps ethernet), and 1000BASE-T (1 Gbps ethernet), but not at 10GBASE-T (10 Gbps ethernet).
It is the interfaces of the devices to which the cable connects that determines the bandwidth of the link. For example, The maximum bandwidth on Category-5e cable would be 1 Gbps. If you try to use it with devices that only work at 10 Gbps, then it will not work at all. Some people may think that the cable will transmit at 1 Gbps in this case, but it doesn't work that way. The interfaces on the devices will send data at frequencies that the cable simply cannot reliably handle, and you will receive garbage at the other end. This is where the comparison to a water pipe fails.
Best Answer
Remember that what you are looking at is marketing material.
The Switch Fabric Capacity is listed in bits per second (bps) and is usually double what it really does since the vendors count full duplex.
The Forwarding Rate is measured in packets per second (pps) and is based on an arbitrary packet size which make the vendor look good.
You really need to dig into each switch individually to uncover the dirt. For instance, I know of a particular switch which has respectable backplane numbers, but when you look at the 10 Gb line cards, each three ports use a single ASIC which is only capable of 12 Gbps. You would need to use one 10 Gb SFP+ and two 1 Gb SFPs on a single ASIC to use it without lost frames.
This is a question for which the answer depends on the make and model of the switch.