An extrasolar Jupiter is a large gas planet that has been found orbiting round another star some where outside our Solar System. Jupiter is the largest object in the solar system excluding the big ball of nuclear reaction, a.k.a. the Sun so its fitting that we refer to gas Extrasolar Planet (Exoplanet) as Jupiters. When astronomers are talking about Jupiters, they are not talking about being exactly like the big planet with a large red spot.
As they are gas supergiants, there is next to zero chance of any of these forms of planets have life. If there is any life, it'll only be microbial as they have been know to survive in the harshest of temperatures on the Earth. For example, microbial life has been found to exist in boiling hot springs in Yellowstone National Park. These habitats have been known to get as high as 140 degrees C, temperatures that would kill humans. Ref: Carleton
A Hot Jupiter refers to a giant gas planet that is close to the star that it is orbiting and therefore its temperature is very high. They can be orbiting closer to the star than Mercury does with the Sun so that their temperatures are far hotter than what you would find on our Jupiter.
Jupiter takes roughly 12 years to make one orbit round the Sun, a Hot-Jupiter would be significantly quicker round its star because it is closer into the Sun.
Our Jupiter is a stationary orbit round the Sun, in so far that it isn't moving closer or further out from the Sun. As orbits round the Sun are not perfect circles, I'm excluding about it being closer to the Sun at certain times. There is a theory that Hot Jupiters were created outside its current orbital plane and migrate inwards. According to some, Jupiter should've moved a lot closer than it has but fortunately for us, it hasn't.
Some reasons why Jupiters move closer into the orbit of the Sun have been put forward such as influence by other objects in its solar system. There could be a larger Jupiter or a brown dwarf that sends the object in closer to the Sun and then is caught in the stars gravity.
HD 80606b is a recently observed Hot Jupiter which is orbiting the star HD 80606 in the constellation of the Great Bear, Ursa Major. It has been shown that the planet is a highly eccentric orbit, coming very close and then very distant to its star every 111 days. The orbit would never take it outside the orbit of the Earth. It is seen as being in the process of migrating inwards. Ref: N.A.S.A
Kappa Andromedae has a Super-Jupiter which is orbiting at a distance 1.8 times the distance between the Sun and Neptune therefore could be called a Cold-Jupiter. There's no indication I've seen that would indicate it was migrating inwards towards its Sun.
The Hot-Jupiter that I'm using as an example is WASP-12b, a hot jupiter that was discovered by the SuperWASP project. The SuperWASP project is a consortium of academic organisations that hope to discover exoplanets using the photo transitory, a method that spots whether the star dims when an object passing in front of it.
WASP-12b is so close to the Sun, it orbits its planet in little than an Earth day. It is slowly being boiled away because it is so close. It has another 10 million years left before its all gone, enough time to build a space ship and say goodbye. The exoplanet might not be alone but there's no other planet in the system so far discovered as of April 2017.
The below is an artists impression of what Wasp-12b looks like close up. Wasp 12 is roughly the size of our Sun for comparison.
A Super-Jupiter is a gas planet that is many times more massive than our own Jupiter. When they talk about being massive, they are not talking radius or diameter but mass as mass is easier to work out. Super-Jupiters are easier to spot than other times of exoplanets on the basis that have more of an effect on the star that is orbiting. When a Super-Jupiter orbits round a star, the Super-Jupiter tugs on the star therefore allowing satellites and telescopes to notice the move of position or darkness caused by the planet.
Jupiter is the second largest object in the solar system, you could fit 1,300 Earths in side it. Ref: N.A.S.A. With that size in mind, Super-Jupiters could fit many more times that amount of Earths inside them. As Jupiters are being discovered all the time, by the time you've got to read this document, a new largest Jupiter will have been discovered.
Those exoplanets that are smaller than our Jupiter and they do exist are known as Sub-Jupiters or Mini-Jupiters. There is a fine line between being a Super-Jupiter and a brown dwarf. If the gas planet has enough mass, it will start nuclear fusion and therefore become a star.
Wasp-17b in the constellation of Scorpius is a large gas giant but incredibly is as dense as a foam cup. In addition to having a low density, it also orbits retrograde probably as a result of a cosmic collision early in its life. Ref: National Geographic