A wavefunction is a representation of the state of a quantum
system. A quantum state is a vector belonging in an abstract space
(the Hilbert space), while a wavefunction is a complex function
given in terms of a Hermitian variable (usually position or
momentum). When "wavefunction" is used unqualified (as opposed to
"wavefunction in momentum space"), it is taken to mean the
wavefunction in terms of position. In case of single-particle
systems, the modulus squared of the wavefunction at a given
position represents the probability density of the particle to be
at that position.