Significantly. Hexes, districts, no unit stacking, resource stockpiles, religion, loyalty. Just some of the new concepts and mechanics in more recent civ games that 1, 2 or 3 didn't have.
Other areas that have changed significantly are e.g. trade, diplomacy and espionage.
Diplomacy in the newer games has a lot more freedom and variety in terms of the deals you can make, what you can trade for what with the AI, etc., but you can't directly exchange technologies any more. (At least not in Civ V.)
In Civ I and II, caravans and diplomats/spies used to be units you moved around the map manually. Then there's the whole city states thing since Civ V (I think), strategic resources that are required for particular units or buildings, significant changes in how happiness/approval is managed, as well as several victory types apart from conquest and space race.
In 90's Civ games (except for SMAC) all the civilizations were also essentially identical in terms of gameplay, except for AI leader parameters and diplomatic stances. Newer games in the series have more differences between civilizations in terms of strategy, at least in theory.
Basically, the core idea is still the same but the details and many individual mechanics have changed a lot.
I just looked at https://www.freecivweb.org/ and one can choose this rule set at the beginning, among some other options. Wasn't the case when I last looked. Play in browser, no setup necessary. WARNING!Timesink!
Civ 2's limited sight distances and "every unit in a stack dies if one unit loses a fight" are pretty good anti-stacking measures until you're well past the inevitable victory watershed line of a game.
