not the best person to ask but to be very generic:

Hardstyle is a Hard Dance Genre that usually plays at 150 BPM (Beats per Minute). there are the beautiful, melodic tracks such as this, this, and one of my personal favorites, this (seriously, i cried a manly tear when i first heard this), and then there is the darker, harder rawstyle such as this (btw atmozfears has had multiple releases on Monstercat as his other alias TVDS and one hardstyle track with In-Phase), this, this, and this one that i like very much, and there's so much more great tracks in this scene. 2007-2010 were the so-called glory years of hardstyle, and those tracks are amazing with produces such as HeadHunterz and Showtek, but music always evolves (this is a subgenre of hardstyle called Dubstyle, which my favorite producer, Obsidia, used to make like this god i love him)

Hardcore is a Hard Dance genre that's significantly faster than Hardstyle, around 160-175 BPM or more. there's happy hardcore such as nanobii's release on Monstercat, but the Hardcore that u posted is the stereotypical hardcore that everyone either loves or hates ¯_(ツ)_/¯ . Angerfist is the most known Hardcore producer, with sick tracks like this

hope i helped and happy listening. i got into the hard scene about 5 months ago so i'm still learning a lot myself, but whats important is that if you like these tracks, then never be ashamed to fucking enjoy blasting them and dance.