Brown Dwarfs are essentially high mass gas giants though. That's the issue, we don't have enough knowledge about them and the limit to which they transition to stars to properly classify them better. They are difficult to find and observe because they don't shine bright comparatively and we only have hypothetical limits to what mass is necessary to ignite.

But yes, lower end mass gas giants like what is in our solar system are definitely not close enough to be considered failed stars in any regard.

But even so, the definition of brown dwarf isn't necessarily set in stone. It definitely can't fuse normal hydrogen, but do you define the lower limit by the physical process, by formation mechanism, or by observational feasibility?

• Physical process: must be fusing deuterium? It's a nice physical process to define by. However, it's basically impossible to tell observationally whether a (potential) brown dwarf is burning deuterium. There are no outward signs. You can often measure mass, and the deuterium burning mass is approximately 13 Jupiter masses, but it depends on metallicity and age. Therefore, if you find an object that's around the limit, you're not sure what to call it without knowing metallicity or age, which is harder to do. Additionally, an older 13 M_J brown dwarf won't be fusing deuterium anymore, so does that mean it started as a brown dwarf and then became a planet when it burned all the deuterium in its core? That's not very satisfying.

• Formation mechanism: formed via disk instability/gravitational collapse (as opposed to core accretion)? There is very likely overlap in masses between high-mass core accretion objects and low-mass gravitational collapse objects. You could therefore have like a 10 M_J brown dwarf via gravitational collapse that has never fused deuterium, but a 15 M_J planet formed via core accretion that fuses deuterium. That's not very satisfying either to have an overlap in mass ranges.

• Observational: use 13 M_J as your cutoff? It's reasonable since that is generally the most observational characteristic that can somewhat distinguish the above scenarios. However, that means some your brown dwarfs formed via core accretion, while some planets formed via gravitational collapse. Similarly, it means that some of your brown dwarfs never fused deuterium, and some of your planets do fuse deuterium. Physically, it doesn't make sense to have either, but observationally, it's a very nice cutoff. Still, this isn't very satisfying either.

As far as I'm aware as a PhD in astronomy in exoplanets, there's not really an agreed-upon consensus among these three choices of definition.