Answer (TL;DR):
False, ionic compounds form between a metal and a nonmetal. This is because metals are looking to lose electrons to get a full outer shell while nonmetals are looking to gain electrons to get a full outer shell.
Step-by-step explanation:
Atoms have a full outer shell when their outermost shell holds the maximum number of electrons. For example, if the outermost shell is the first shell of the atom, it can hold up to 2 atoms. When this shell holds 2 atoms, it is considered full. If the outermost shell is the second shell of the atom, it can hold up to 8 atoms. When this shell holds 8 atoms, it is considered full. This can also be referred to as an atom "gaining a complete octet." The reason that atoms want a complete octet is to become stable and less reactive.
Let's say an atom with 3 shells has only 1 electron on the third shell. It doesn't have a complete octet and it wants to gain one. The third shell can hold up to 8 electrons. So, to gain a complete octet, the atom can either gain 7 electrons or just lose the 1 that it already has, which is the easier option. This is the case with metals and the opposite goes for nonmetals.
Because metals want to lose electrons and nonmetals want to gain electrons, they form compounds with each other.
I hope this helps!