They are similar, but you have pointed out the key difference, the down-time. The cost is a big difference as well.
A fault tolerant environment has no service interruption but a significantly higher cost, while a highly available environment has a minimal service interruption.
Fault tolerance relies on specialized hardware to detect a hardware fault and instantaneously switch to a redundant hardware component—whether the failed component is a processor, memory board, power supply, I/O subsystem, or storage subsystem. Although this cutover is apparently seamless and offers non-stop service, a high premium is paid in both hardware cost and performance because the redundant components do no processing. More importantly, the fault tolerant model does not address software failures, by far the most common reason for downtime.
High availability views availability not as a series of replicated physical components, but rather as a set of system-wide, shared resources that cooperate to guarantee essential services. High availability combines software with industry-standard hardware to minimize downtime by quickly restoring essential services when a system, component, or application fails. While not instantaneous, services are restored rapidly, often in less than a minute.
Many sites are willing to absorb a small amount of downtime with high availability rather than pay the much higher cost of providing fault tolerance.