A rescue craft is a boat, ship or aircraft used in rescuing.
The most common are Lifeboat (rescue) for Inshore and closer to shore rescues. For operations further out from shore helicopters & ships are mainly used.
Most Government agencies rely on larger ships for rescues further from shore such as Royal Navy ships in the United Kingdom and Coast Guard Cutters used in the USA (Although the UK Coastguard does use larger vessels to tow ships in distress). Similarly the UK uses both the Royal Air Force SAR and UK Coastguard for helicopter rescues and the USA uses the United States Coast Guard for theirs.
Rescue craft Wikipedia
There were attempts as early as the 14th century to aid shipwreck victims with the Chinese training in resuscitation for the drowning, as well as Portugal and Sweden in the 1690s ordering that ships should be sent to sea to rescue shipwreck survivors, but the first mention of lifeboats was in China where boats were used to rescue people from the rivers in 1737.
The development of the seaplane meant that aircraft could be used to rescue people but was limited as they could not land or take off in heavy seas.
Helicopters overcame this problem as they were able to hover over the victim and give aid by dropping a line to them with either a basket or diver to assist their extraction.
Many types of boats and ships are used, ranging from 2 man inflatables, such as the IRB's, through RHIB's all the way up to larger purpose built vessels.
For offshore and far from coast rescues operations most countries rely on Naval or Coastguard ships for these operations
For submarines which have got into difficulty there are highly specialised rescue submarines and support ships such as the NATO NSRS and the USA's DSRV
There are still smaller boats which may be used on inland waters such as lakes or estuaries where the waters are generally calmer and shallow. These boats are often hand powered.