Games that use a feeling of dread and anticipation to scare and startle the player. Terror is the suspenseful moments where the player is anticipating something will happen. Horror is where one sees the object that causes the terror.
Horror games works best when playing alone, both from other players and other characters in the game. With another player you can talk about things and analyze them and it makes things less scary. Alone you can only talk with yourself and as crazy people know it is the fast track to madness. Other characters in the game makes you worry about their safety or they are immortal for the story and you use them as bullet sponges. They can also be incompetent and always get in the way. They can also be the type that never stops talking. Yes Metro 2033 I'm looking at you.
After you have your shotgun and the fifth zombie is dead it is businesses as usual. By making the player less powerful then is normal in games one can keep the level of terror high. This can be done by making the ability to fight back less common. Ammo can be scarce, reload time long, weapons can break fast and be uncommon. Another option to take away the ability to fight at all and only give the player the option to hide and flee.