How are haplotype blocks different from genes?
Haplotype blocks may cover more than just one gene.

While positions within a gene are also in high linkage disequilbrium (or well correlated) with each other, this phenomena of high LD may extend beyond the gene body and overlap with the next gene.  A good visual representation of this comes from Jeffreys et al. in the figure below:



Red means more LD, black means zero LD.  Each point in the heatmap is essentially a pairwise correlation between two points in the genome.  Therefore regions of red represent regions of high LD or haplotype blocks.  Going from left to right we can see that each gene appears to be in its own block of high LD.  However, the genes PSMB9 and TAP1 appear to be in the same block.  Other examples exist as well, a great source is this review.