In a lot of movies and video games portraying WW2, we see a lot of scenes of both sides fighting against each other in rather short distances. When watching modern war footage however, it appears that firefights occur from longer distances. A few modern soldiers have said that they have never actually SEEN the enemy during engagements. Was this the case back then? Or were the movies right about how close and intense firefights commonly were?
Because WW2 was a globe spanning war, you can't really say that there was an average experience of combat like in more localized wars, such as Vietnam or Afghanistan. The experience of a U.S. marine fighting in dense tropical jungles might be unrecognizable to a Soviet soldier fighting on wide-open frozen plains, to give just one example.
Terrain and environment would have played the biggest factor in what subsequent fighting would be like. German soldiers reported that in the close-quartered combat of Stalingrad the enemy was often so close that they could shout out to the enemy, and that opposing trenches might be as close as 15 feet away. Compare this with the fighting of Normandy in 1944, where most fighting occurred in open fields and hills which resembled the experience you described: Shooting at enemy pillboxes and dugouts without seeing the enemy face to face. The point being that there is not really a general example one can point to and say "This is what fighting in WW2 was like!", but more like many different examples that show what fighting in that particular battle of WW2 was like.
Generally, to be seen while in effective range of the enemy's weapons is to invite death. This is nothing new - this basic principle goes back to the Stone Age. What has changed over the last century and bit is the range and lethality of the weapons. We now have weapons with effective ranges of many kilometres, such as artillery, and exposure anywhere in the forward few kilometres of the battlefield can be deadly. The main defence for infantry on the battlefield is invisibility, either by making use of natural cover and concealment, or by creating cover and concealment (trenches, foxholes, camouflage). When there isn't an attack in progress, soldiers on both sides are hiding. It's usual to not be able to see the enemy.
Attack requires exposure, which means a lot of risk. First, attackers often try to make use of cover as much as possible. Second, the "fire" part of "fire and movement" is used to keep the defenders head's down, preventing them from being able to effectively shoot at the attackers. Thus, even during an attack, it's possible to not see the enemy. For an example showing both of these - use of cover, and use of fire and movement - see
Note the comment at 6:48 about the importance of camouflage: "Notice the white hand showing through the brush. These Germans are flirting with trouble. They'll be out of the war quickly if they don't smear some dirt or mud on their hand.".
Some weapons have short ranges, and require getting dangerously close to the target. Limiting exposure to fire is essential! For a post-WWII example, see
Compare the infantry attack linked above with this very cartoonish movie battle scene, the Khalkhyn Gol (Nomonhan) scene from the Korean movie My Way (2011):
It appears to be much more influenced by modern computer games than by real-world warfare.
For reinforcement of the importance of not being seen, see this footage of a sniper in action in modern simulated battle (airsoft):