‘As’ and ‘like’ pose a number of problems, since Czechs simply use ‘jako’ for both. In English, it is more complicated. We use ‘like’ for senses, e.g. . “She smells like a homeless”, or “This tastes like chicken.”
We also use ’like’ to mean ‘example.’ So, you might say, He enjoys sports like football and tennis.
But one case where you don’t use ‘like’ is with comparatives using the word ‘same.’ A lot of my students will say something “He is the same like me”. But this is wrong. You need to use ‘as’.
So, correct is to “He is the same as me”, or, as in the very first “My sister is the same size as me.”