Both describe transitions, but "across" is related to traversal, "through" is related to penetration, going into something. For example, "he walked across the bridge" - meaning, he passed over the bridge. "he walked through a tunnel" - meaning, he passed inside the tunnel.

through |θroō| preposition & adverb 1 moving in one side and out of the other side of (an opening, channel, or location) : [as prep. ] stepping boldly through the doorway | [as adv. ] as soon as we opened the gate, they came streaming through. • so as to make a hole or opening in (a physical object) : [as prep. ] the truck smashed through a brick wall | [as adv. ] a cucumber, slit, but not all the way through. • moving around or from one side to the other within (a crowd or group) : [as prep. ] making my way through the guests. • so as to be perceived from the other side of (an intervening obstacle) : [as prep. ] the sun was streaming in through the window | [as adv. ] the glass in the front door where the moonlight streamed through. • [ prep. ] expressing the position or location of something beyond or at the far end of (an opening or an obstacle) : the approach to the church is through a gate. • expressing the extent of turning from one orientation to another : [as prep. ] each joint can move through an angle within fixed limits. across |əˈkrôs; əˈkräs| preposition & adverb from one side to the other of (something) • expressing movement over a place or region : I ran across the street | traveling across Europe | [as adv. ] he had swum across. • expressing position or orientation : they lived across the street from one another | the bridge across the river | [as adv. ] he looked across at me | halfway across, Jenny jumped. • [as adv. ] used with an expression of measurement : can grow to 4 feet across. • [as adv. ] with reference to a crossword puzzle answer that reads horizontally : 19 across.

across the road through the tunnel Easy!

Across means from one side to another anf through means across from inside e.g. to see through a window

Across refers to travelling with open space around you. Through generally implies that something surrounds you (a door frame, a tunnel, something that is more enclosed.) I hope that this helps!