The first three seasons are recorded without the use of Discord or any voice chat. Everyone participating just sits in the same room as each other. You can tell when someone talks about what they saw on another's screen. The reason for this is that at the time DaZapow wasn't allowed to vc on discord.
Zapow calls these seasons the "IRL" seasons and sees them as their own separate thing. This is why the first "discord" season is Terraria #1 and not Terraria #3.
DaZapow and XanChan are the only members of the original IRL seasons that watch Hardcores. Dragonboy watched part of PBG's Terraria Hardcore 3, but that's it.
The name "Zapowcore" wasn't created until recently, leaving the first two to not bear the name.
The new name was originally Zapcore. But it was taken by Zap.
Terraria HC #2.5 can be shown as a trainwreck here.