I went and compared a bunch of my gear to make my own technicality test playlist.
Anyway, you should temper your expectations for $30 IEMs and be very skeptical of audiophile hype trains. No manufacturer is going to leave money on the table by charging that little for an IEM they know sounds high-end given how absurdly deep people's pockets go in audio land, although you should be warned that many of them do overestimate their products' quality and overcharge.
No fully agreed-upon definition for either of these as far as headphones go, especially not for the latter. Saying all you have to do is accurately simulate human HRTF and PRTF is easy, actually doing it is not. Trying to jam an approximation of loudspeaker acoustics into a pair of ear cups also leads to design compromises needing to be made. Manufacturers like Hifiman, Sennheiser, and DCA do try to tune to their own target curves that they believe sound neutral, and many headphones do feature angled drivers and such to attempt to replicate speaker/ear interaction.