A clock crossing bridge is like a bus bridge, but has different clock domains on each side. Two quartz crystal oscillators, each of 10 MHz frequency will actually be different by tens of Hz and drift with temperature. Atomic clocks are better: accuracy is one part in ten to the twelve or better.
A simplex clock domain crossing bridge carries information in only one direction. Duplex carries in both directions.
Because the saturated symbol rates are not equal on each side, we need a protocol with insertable/deletable padding states or symbols that have no semantic meaning. Or, in higher-level terms, the protocol must have elidable idle states between transactions.
Clock domain crossing is needed when connecting to I/O devices that operate at independent speeds: for example, an Ethernet receiver sub-circuit works at the exact rate of the remote transmitter that is sending to it. Today's microprocessors also have separated clock domains for their cores viz their DRAM interfaces.
The data signals can also suffer from metastability, but the multiplexer ensures that these metastable values never propagate into the main logic of the receiving domain.
Simplex: can never be sure about the precise delay.
100 percent utilisation is impossible when crossing clock domains. The four-phase handshake limits utilisation to 50 percent (or 25 if registered at both sides) Other protocols can get arbitrarily close to saturating one side or the other provided we know the maximum tolerance in the nominal clock rates. Since clock frequencies are different, 100 percent of one side is less than 100 percent of the other or else overloaded.