Ten's speech about the "other guy goes swanning off" gave it a different spin, that the person is more 'dead' than we previously thought. Yep, memories, and basic physical structure remain, but most of the body's cells get in effect rebooted.
Yeah, I think that was the first time the Doctor admitted that whatever incarnation he's in does indeed die when he regenerates, with someone else then acquiring his memories and experiences afterward. The same Time Lord, yet not the same.
But thinking about what regeneration feels
like, I think since the show's revival, regeneration might feel like being set on fire both inside and out.