Development was handled mostly in-house by Valve, with help from Turtle-Rock Studios and Hidden Path Entertainment [1]. It used Valve's new engine, Source.
Gameplay is the same with other games, mainly weapon recoil and AI being changed. It allowed for new physics not achieveable in GoldSource, which was a heavly modified version of Id Software's Quake engine, though early source games, such as CS:Source still have GoldSource and Quake engine code in them [3]. CS:Source also recorded player stats and achievements [4]. It was one of the earliest games to use Source on Steam, other one being Half Life 2. With the new Source SDK, modders could also create bigger maps, gamemodes, and models for CS:Source.
Screenshot 1 from https://www.gamingcfg.com/screenshot/Counter-Strike-Source-de_dust2-2, screenshot 2 from https://lutris.net/games/counter-strike-source/, screenshot 3 by Turner Land.