Is a metal's work function, #Phi# and first ionisation energy the same?
No. They are similar but have a subtle difference.
The ionization energy (IE) is qualitatively defined as the amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated gaseous atom to form a cation.
Thus in order to define Ionization energy, one has to consider an isolated atom. In that case, to remove an electron, the interactive forces you have to counter are the electrostaic forces within the atom.
However, the work function is the the minimum quantity of energy which is required to remove an electron to infinity from the surface of a given solid, usually a metal.
This time in order to remove an electron from the surface, you have to counter not only interactions due to one single atom but due to a number of other positive atomic centres placed in the crystal. Particularly, in metals, you remove the electron from the conduction band which has various distributions of energies. The minimum energy required (i.e. for the most loosely bound one) is the work function.