Atomic orbitals and $\psi:$ According to wave mechanics, the atomic orbitals can be expressed by wave functions $(\psi)$ which represent the amplitude of the electron waves. These are obtained form the solution of schrodinger wave equation.

Molecular orbital and $\psi$ and $LCAO$ : Schrodinger wave equation can not be solved fore any system containing more than one electron, molecular orbitals which are one electron wave functions for molecules are difficult to obtain directly from the solution of Schrodinger wave equation. To overcome this problem, an approximate method known as linear combination of atomic orbitals ($LCAO$) has been adopted.

$LCAO$ means method for solution of molecular orbitals having more than one electron by Schrodinger wave equation.