I don't know what else to say... there is so much confusing, and possibly straight-up-wrong information on those sites. One of the many flaws of the internet...
Most rocks won't straight-up kill your fish. Usually when people are worried about "aquarium-safe" rocks, they are concerned about rocks that may affect water parameters like hardness (GH, KH) and pH.
There are a lot of carbonate rocks (limestone, dolomite, travertine, tufa, coral, calcite, marble, and a few other terms I'm forgetting), that aren't poisonous or anything, but will react with tank water, dissolve slightly, and raise GH, KH, and pH. Most of these are some form of calcium carbonate(CaCO3), maybe some magnesium carbonate(MgCO3), or some mix of the two. Calcium carbonate is far more common. When these rocks are placed in water, a small part of them dissolves, releasing carbonate ions (-CO3), and magnesium/calcium ions (Mg+/Ca+). Carbonates will directly raise the KH(carbonate hardness) of your tank, and possibly react with any acids present, leading to a raise in pH. I'm a bit more ignorant on the chemistry of what happens with the magnesium/calcium ions (Mg+/Ca+), but at the very least, they will raise the GH (general hardness) of the tank. They are also important for plant and beneficial bacteria growth, so there should almost always be at least some of these in the tank.
If you have hard water coming out of your taps, this might not be that big of an issue, as people have been keeping (and sometimes even breeding) softwater fish in hardwater set-ups for some time now. On the other hand, if you are going for a hardwater fish, like rift-lake cichlids, or some live-bearers, then these rocks would pose no problems, and possibly some benefits for you.
If you are trying to maintain a softwater environment, and have soft tapwater (or are using RO/DI or pretreating with peat, or whatever...), then you should avoid these rocks.
This is a very broad generalization, but most igneous rocks will be safe for any tank-type. Granite, basalt, obsidion, rhyolite, lava rock, pumice, etc.
Most metamorphics are safe (gneiss, schist, slate, etc.), but some are potentially problematic (marble, and some others I'm not remembering right now...), and some will be straight-up toxic (mostly metal ores).
Sedimentary rocks are a confusing mixed bag... Usually sandstone is silica sandgrains in a matrix of... something? Silica is completely inert and fine for any tank setup, but the matrix can be any number of substances, and a silicate sand stone with a carbonate matrix isn't unheard of...
tl,dr; I'd avoid rocks with metallic or really bright colorings - might be a metal ore if you don't have more specific information. Like Diana mentioned, take something steel, and try to scratch the rock. If you can't scratch it, it's probably a silicate and fine for whatever. If you can scratch it - try testing it with acid (where you scratched it), if it bubbles, it's a carbonate, and should only be used if you have a hardwater set-up.
And try to ignore the names in petshops and stoneyards. They have about as much to do with the composition of the rock as my dinner did.