The big difference here is there is no expectation that anything you run into is pre-determined as beatable. You think and act just as you would if you were there dressed in that armor, carrying that sword, having had prepared those spells. There are no arrows hovering in the air on where we are to go or what we are to do. Nor are there bright red lines drawn on the ground saying "you're leaving Level 1 area" "entering level 5 area". If we're not cognizant of our surroundings and the thinking twice about the repercussions of our actions (and sometimes just bad luck - not dice related), we run into "really bad things" like dragons. Of course, we also slaughter kobolds and goblins and zombies without thinking too hard and sometimes getting in trouble for it. Mostly though those fights are just mop ups.
I run things in a somewhat similar fashion; I make a point of including encounters with critters that are way too tough for the PCs, and other encounters with critters that the PCs can walk right over. (If the PCs pick a fight in the latter case, I don't even bother to play out the battle; I simply announce, "Okay, you crush them. They're all dead. What are you doing next?")
However, I do put some thought into the tough encounters in order to avoid "unfair" TPKs - which is to say, TPKs that the party has no reasonable way to foresee and avoid. Generally, I try for one of two things with a "too big for you" encounter; either a) it's obviously something bigger than the party can handle, or b) it's something that won't kill the PCs outright if they attack it. And in either case, I make sure to give them the option to avoid combat.
An example of type a) would be when my 4th-level PCs were going through a dungeon under a ruined dwarven citadel, and decided to investigate the tunnel that led to the Underdark. They found a cave with a hydra in it; a fortified outpost manned by troglodytes (and I made sure to let them know that troglodytes do not build fortifications, but are commonly used as slaves by more powerful races, such as drow and illithid, who do); and a deep, deep tunnel leading to a pit surrounded by eight lich vestiges chanting. They took the hint and retreated. If they had tried to pick a fight down there, I would have let natural selection take its course.
An example of type b) would be when the same party at 3rd level ran into an ogre named Throog. Throog was a herdsman who kept reindeer, only his reindeer kept dying and he was looking into alternative herd animals. As soon as he saw the party, he announced that they were his new herd. Talking or tricking their way out of this situation was easy, since Throog was not intended to pose a difficult challenge - he was there for fun and color. However, I did consider that they might decide to pick a fight, since a single ogre was not clearly out of their league. Throog was an 8th-level solo, so he would have wiped the floor with them at the time; however, because they were his "herd" and a good herdsman cares for his animals, he would have stopped to make Heal checks and fix them up afterward.
Of course, there is also situation c), where the party has to find a way to beat enemies who are obviously way out of their weight class for a straight-up fight. I haven't done a lot with this lately, but I have in previous campaigns, and I'm thinking about some possibilities...