@ShadowLightMew I believe the distinction you're looking for is whether the shiny Pokemon from the rom are 'legit' or 'legal'.
'Hacked' is often used to refer to any Pokemon that was obtained through unofficial means; the shiny rom 'mons are definitely hacked.
'Legal' means that the Pokemon's data - location, stats, trainer id etc. - all match those of a legit Pokemon. The Pokemon could
technically be obtained officially regardless of whether it actually is. Legal hacked Pokemon are impossible for the GTS etc. to pick up, but we can often infer that a legal Pokemon is likely to be hacked due to the sheer improbability of encountering it (e.g. 6IV unbreedable shiny Pokemon; a couple of legit ones may exist somewhere in the world, but probably not on the GTS). The shiny rom 'mons are mostly legal, with the exception of shiny-locked species such as Reshiram.
'Legit' Pokemon are ones that have been obtained the official way - they have been caught/bred/obtained in-game, with no rom hacking/cheating/etc. methods. Legal Pokemon include official distributions by the Pokemon company, and this is often the only way to obtain legit mythical Pokemon or certain Pokemon/move combinations (e.g. Happy Hour). For example, the Arceus from the distribution that's going on right now is 100% legit. However, if this Arceus is cloned, the clone is
not legit as cloning is not an official part of the games. If someone hacked their old gen 4 game to unlock the Azure Flute, the Arceus caught there would also
not be legit, despite being caught in-game, as the Azure Flute was never officially distributed. All legit Pokemon are legal, but not all legal Pokemon are legit. The shiny 'rom mons are most certainly not legit!
You'll find differing opinions as to whether legal hacked Pokemon (like those from the shiny rom) are okay to use or not. Some people feel that if the Pokemon is technically obtainable in the games, then it's okay to not waste time breeding the right IVs. Others will not agree with that, but will be okay with cloning Pokemon that cannot be obtained otherwise - for example, Volcanion was never distributed in my country (Australia) so anyone from here that wants one will pretty much have to settle for a clone. Some people do not want any hacked Pokemon at all. All these opinions are okay! However, if you're trading, it's good form to be open about whether the Pokemon is hacked/cloned/legit so the person you're trading with can make an informed decision.
TL;DR: All Pokemon caught on the shiny rom will be hacked; almost all will be legal with the exception of Reshiram and Zekrom, and none will be legit.