The major difference between these two lies in easy access to your funds. A savings account is opened to make long-term deposits and receive interest on them. It means that you don’t use your money but receive interest instead. Meanwhile, the bank is using these funds for giving loans to other people, for instance.
A current bank account is opened for everyday use. You can deposit it and withdraw funds as much and as often as you want to. There’s no interest here, but the limits for most transactions are quite high.