The question of ‘meteorite’ versus ‘meteowrong’ is common, because people have incentive, and fertile imaginations. As you can guess, most bystanders are finding meteowrongs.
You had enough background and foresight to check using a magnet- progress, but not conclusive. Some earthly minerals are magnetic, while some meteorites (most achondrites, including the HEDs- not that rare) are nonmagnetic.
Some meteorites show fusion crust, and possibly regmaglypts, some don’t. Virtually all recovered meteorites have experienced some breakup and/or erosion during entry, and have fresher surfaces. This includes the rear surface of a meteor that by chance had a stable shape and didn’t tumble, and the interiors of weak meteorites. And let’s not forget chipping upon ground impact, let alone weathering on terrestrial exposure.
If one of your samples shows a fresh surface due to fracture/chipping, petrology may be taken as one kind of evidence. Most (but not all) meteorites are breccias, possibly gabbros- they’ve been formed by unifying pebbles, dust, possibly cobbles on a large parent body. This may be visible as a grain texture… or not. You may need a magnifier for fine breccias, and there are meteorites that are monolithic (irons, rare examples of chondrites, and again, some of the HEDs). The oddest grains are chondrules- sub-millimeter to ~mm spheres, spheroids, plus fragments and composites. These have few terrestrial equivalents. Unfortunately a fair number of meteorites never had/have chondrules.
Density is a reasonable test… except it, too, is not conclusive either way, and has testing issues. It’s easy enough to weigh a sample, but not to state the volume of an oblong/composite/whatever. Meteoriticists use, instead of water displacement (might affect some minerals) a ‘tank’ of fine plastic beads. The before-after difference gives volume, and it’s straightforward- though possibly annoying- to clear all beads afterwards. And who knows, there might be some stereophotometry now that can give some volume number if the object is a suitable shape. In any case, most meteorites are significantly denser (~3.2 g/cc) than most Earth rock… except the meteorites that aren’t.
Ultimately, you’ll need a chemical assay to identify the meteorite class, and thus positively ID the sample as a meteorite. Most meteorites have ‘chondritic’ composition- no loss of siderophiles to a core, very low loss of lithophiles to a crust, low loss of chalcophiles, and more atmophiles than Earth rock. …Except irons, which were the core, HEDs/Martian/Lunar meteorites which were the crust, and miscellaneous other achondrites. A decent chem analysis would still determine irons, ureilites, aubrites, etc. There’s a chance a detailed analysis would be necessary, but the initial results would likely point that out, rather than reject the stone.
Good luck with your two examples, but be prepared for disappointment. Even working meteoriticists can’t tell in the field, and await lab results for a positive ID.