Difference Between Low Silver and High Silver

Hi guys, So I've heard many comments about low silver and high silver. People say people in both divisions are bad at the same level, but at the same time, as you go up in divisions, you'll see players with better mechanics and play style. Regardless of which one is more accurate, I personally feel like I have more problems with the higher silver players than the lower silver players. Generally against low silver players, I win in lane as long as I counter or use my plan to win their champs. However against higher silver players, I still somehow end up losing lanes even though my champion counters their champion and yeah. Do any of you players personally have this kind of problem, and if so and if you know the answer, how would you get past this situation? How would you fight against high silver players differently than low silver players? Thanks a lot! P.S. As you might see, I am only level 20, but I used to play on a level 30 account. Also, I don't mean to brag that I'm good or anything, but I played against high silver players in this account.