The planet Jupiter is a large mass of gasses, and brown dwarf stars are a large mass of gasses. But the difference lies a little bit in the diameter and a lot in the mass. Jupiter is a massive planet, 10 times as thick and a thousand times heavier than Earth. Mercury is the smallest planet, less than 1/2 the width of Earth and five percent the weight of Earth.
But in other solar systems, more massive planets than Jupiter have been discovered. These gas planets are getting near the size of a brown dwarf in their width. But they still do not have enough gas to be a brown dwarf. There is debate in the scientific community as to the difference between a really large gas planet and a brown dwarf. Brown dwarf stars do not have an active stellar fusion reaction in process, but the coolest brown dwarfs are as warm as Earth. This is peculiar because we know that the Earth gets heat from the Sun, and heat from internal nuclear reactions. Brown dwarfs seem to have neither the heat of a nearby star or the heat of a nuclear reaction to rely on.
In the cold depths of space, Jupiter has a surface one hundred degrees below zero. But we think the deepest interior of Jupiter is very hot. This is likely caused by the friction of compressed gasses, compacted by the force of gravity.
A brown dwarf has a surface far warmer than Jupiter. We think some brown dwarfs harbored some fusion at some point. We also believe they are cooling, and often a radiant brown dwarf is very young, much younger than Earth. Theories about the existence of brown dwarfs are decades old, but the best real astronomical evidence is within the last two decades.
We once thought there may be as many brown dwarfs as there are stars, but now we think stars outnumber brown dwarfs by at least five to one. But astronomically, stars give us a bright light to study, as opposed to only a tiny glow.
Black holes were once just a theory, and physicists studying gravity and the mass of large gas planets and small stars thought that something like a brown dwarf existed. Now we have seen them, but questions remain. How many of them lit fusion at a point, are cooler and darker ones still not seen? A key element to study in brown dwarfs is lithium. Lithium is present in some brown dwarfs, and may indicate some fusion at some point.
But if many more brown dwarfs are much older, much cooler, darker and harder to see, we don’t really know yet how much we know about brown dwarfs.
Wikipedia has more up to date information about brown dwarfs.