Another important thing was how almost all character class powers were focused on tactical combat, and they took up a very large portion of the PHB. Non-combat stuff was mostly the domain of skills (including skill challenges) and ritual magic. So for example, the defining abilities of a druid would be elemental blasts, plant manipulation, and shapechanging into fierce beasts, but not things like Animal Friendship, Control Weather, or Commune With Nature – those are rituals and available to anyone with the Ritual Caster feat and the Nature skill.
Yet another thing that made 4e feel more tactical was monsters. In 3e, monsters were built much like characters: start with a monster type and a number of Hit Dice (similar to class + level), add in the effect of ability scores, feats, and possibly gear, generate stats from those, and compare the end result to other monsters to see how difficult it is. This was a method that looked good on paper and seemed "fair", but it could create monsters with some real weirdness to their abilities (e.g. the ogre mage).
In 4e, monsters are instead based on level and a distinct combat role: artillery, brute, controller, lurker, skirmisher, and soldier, with some having an additional leader sub-role. The monster's stats and abilities would be based on its role and level, so a Brute would have a lot of hit points, a low AC, a low attack bonus, but hurt like heck when they connect. A lurker would have a low number of hit points, generally moderate stats, but some ability to deal extra damage to vulnerable targets. And so on. The monster stats were very combat-focused – monsters in older editions often had lots of non-combat or semi-combat abilities but in 4e the idea was that sure, the black dragon might have the ability to foul water sources, but that's something that happens off-screen so it has no place in the stat block.