How is partial melting related to fractional crystallization?

Partial melting occurs in rocks because the different minerals that compose rocks have different melting points. For example, felsic minerals (e.g. quartz and feldspar) melt at around 700 degrees Celsius while mafic minerals (e.g. pyroxene and olivine) melt at around 1200 degrees Celsius. Therefore, felsic minerals will melt first leaving the mafic minerals solid.

Fractional crystallization occurs when minerals from a magma cool and crystallize out of the magma. The first crystals to melt in partial melting will be the first minerals to crystallize out when the magma begins to cool. Therefore, mafic minerals will crystallize first, followed by felsic minerals.

Both partial melting and fractional crystallisation tend to produce a more felsic magma than their source rocks.

The difference is simply that they are the reverse of one another, heat it up, cool it down. Things that melt first solidify last and separate from one another.