Homologous recombination is the process by which two chromosomes, paired up during prophase 1 of meiosis, exchange some distal portion of their DNA.
Crossover occurs when two chromosomes, normally two homologous instances of the same chromosome, break and then reconnect but to the different end piece.
If they break at the same place or locus in the sequence of base pairs, the result is an exchange of genes, called genetic recombination.
This outcome is the normal way for crossover to occur.
If they break at slightly different loci, the result can be a duplication of genes on one chromosome and a deletion of these on the other.
This is known as an unequal crossover.
If chromosomes break on both sides of the same centromere and rejoin to exclude the centromere, the result can be one chromosome being lost during cell division.