Champions can be easily split into three types, early game, mid game, and late game champions.
Early game top laners shine right off the bat. Their goal is to get a quick lead, take the enemy tower, and start roaming and force the lane phase to end. They fill the top lane role, but most of their strength comes from their ability to impact the other two lanes.
Mid game champions, which are arguably the most common, have a few more options. With a slightly larger lead than an early game champ needs they can roam around just the same, but they can also set up shop in the top lane for a long time. From my understanding their goal is less of getting themselves ahead, but to set their opponent behind. They waste time and zone the enemy until the team fight phase begins, where their opponent either groups and falls even further behind or stays top to catch up and leaves their team at a disadvantage elsewhere.
Late game champs act similarly to most mid game champs, however their goal is to extend their lane phase. They can often trade well in 1v1s, but not so well in group combat. They force their opponent to babysit them, or else they can adopt a full on split pushing strategy. These are the champions who truly shine in your 20 minute mark scenario.
The key thing to remember from my first post is that top lane is flexible. It has many different styles of play and the role itself isn't even tied to it's location on the map. Some top laners barely ever go top lane outside of the first 10 minutes of the game. It's uncommon, but it does happen. The above type of champions are really just an over-generalization to help my point come across, as top lane is just too volatile a role to fully sum up in a short manner like that.
To put it simply the location of top lane is important at 18 minutes and on, but the role is flexible enough to shine at any point of the game.