halacha - Is marriage without ketubah considered marriage, concubinage, or kiddushin she’einah re’uyah le’biah (marriage that cannot be consummated)?

Is marriage without ketubah considered marriage, concubinage, or kiddushin she’einah re’uyah le’biah (marriage that cannot be consummated)? I have read a number of different things suggesting each of the three. In the discussion here about concubinage, it was suggested that concubinage=simply marriage without a ketubah, so marriage without a ketubah=concubinage. But I have also read that marriage may be contracted without a ketubah: either through biah or a ring. Finally, I have read one source suggesting that the couple may not have relations without a ketubah; thus, a marriage without a ketubah is a kiddushin she’einah re’uyah le’biah. Which is correct?