No. "liczba", as Wiktionary says, is "a number" as an abstract entity. So it's what we use in mathematics, it's what we'd use to describe an amount of something, etc.
"numer" is "used to show the rank of something in a list or sequence". So for example, the room number 7. The number you had on the attendance list of your class in school. The number on the back of the footballer's shirt. The number of the house/flat etc. Also a telephone number.