If gaseous planets have solid core, can they theoretically be considered as rocky planets? I read that gaseous planets such as Jupiter and Saturn, have a solid core deep inside. So, I wondered whats the difference between them and rocky planets apart from the fact that they have - what can supposedly be considered, a very thick atmosphere, and that their atmospheric pressure would probably be too high.

Is there any other difference which I am missing? I mean, if we go by definition, couldn't all their gaseous content, be considered as an atmosphere?
As a general rule, a gas giant planet is large enough that it retains a lot of hydrogen and helium, such as Jupiter and Saturn.  Their chemical makeup is similar to the universe, nearly 90% hydrogen.

Ice giants, like Uranus and Neptune are made up of material more similar to comets, lots of ices like H20, CO2, CH4, NH3 are the primary 4 ices that form into bodies beyond the frost line, but neither Uranus or Neptune have much free hydrogen or helium, either because they're too small or because of where they formed, to close to the sun where it was too hot for them to retain or keep the lightest 2 gases.

As a general rule, in addition to your definition, one possible definition, of a gas giant is an abundance of hydrogen.

When we get a bit of better look at planets in other solar systems, some of the terminology might need to change.    Super-Earths with a lot of water would be similar to hot Neptunes.   Any very massive planet that is able to collect and retain massive amounts of hydrogen will look like a gas giant, whether it has a super-earth origin or not.    Perfect definitions aren't possible.