Answer:
Being distant cousin to oak trees means that in the phylogenetic analysis we might have a common ancestor with the oak tree in the past. Phylogenetics is the branch of biology which depicts the evolutionary relationship among organisms.
The phylogenetic connection with the oak tree is somewhere far away and we do not share an immediate connection with the oak tree.
On the other hand, being first cousin means that there might be a connection ancestor for the different organisms in the near past.