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For a gas body to be a star, it has to reach a mass so that the density of the core regions becomes high enough for the nuclei of the atoms to overcome their mutual repulsion and begin to fuse. For hydrogen, that starts at around 75-80 Jupiter masses, where the internal temperature has reached around 7-8 million K. That is when the object can be called a star, in the proper sense. Brown dwarfs, which are below that mass limit, cannot fuse hydrogen in any sustained fashion and so are not stars. They have been called failed stars, which they are in a sense. But in strictest terms, they are not stars but nor are they planets. Some of the heavier brown dwarfs can fuse lithium and deuterium for a short while...deuterium burning starts once a body passes 13 Jupiter masses (at around 1-2 million K for the core temp) and lithium burning occurs in bodies over 45 Jupiter masses (core temps around 4-5 million K). These episodes don't last very long as there's not that much of either inside stars to begin with, plus they fuse rather quickly.
Jupiter and Saturn are nowhere near heavy enough to be called brown dwarfs, let alone stars. They never gathered enough mass to become either of them.
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