Half-Life is based on the GoldSrc engine, that has spawned more add-ons that we can count. For example, Team Fortress, Counter-Strike, and Opposing Force
just to name a few.
Half-Life: Day One is the initial pre-release demo of Half-Life. It was designed exclusively for OEM partnerships and was often bundled with graphics cards. It was never available to the general public. Half-Life's proper demo (available free to the general public) is Half-Life: Uplink, which was released several months after the full game. - Combine OverWiki
