What I knew about the ようにする／なる is 'to make sure'
What are the difference in usage? Please give me examples of each
野菜を食べるようにする (I) make it a point to eat vegetables
野菜を食べれるようになる (I'll) be able to eat vegetables
The main difference is the former expresses a will to do something in the present, while the latter expresses a future state (in what something ends up).