The result of gene crossing over during synapsis is recombination, not independent assortment. Recombination occurs much later, in the prophase-1 stage, whereas independent assortment as Mendel defined it occurs in anaphase-1. So even though the result of the crossing over is the same as independent assortment, it would never be classified as such, it would be classified as recombination.
In terms of gene linkage, we can have various degrees of linkage. Complete linkage means the gene pair is always inherited together, and when only inherited together a percentage of the time this is incomplete linkage. Gene pairs are classified as linked if fewer than half the gametes from a double heterozygote cross are recombinant.