Isoschizomers are pairs of restriction enzymes specific to the same recognition sequence. For example, Sph I (CGTAC/G) and Bbu I (CGTAC/G) are isoschizomers of each other. The first enzyme to recognize and cut a given sequence is known as the prototype, all subsequent enzymes that recognize and cut that sequence are isoschizomers. Isoschizomers are isolated from different strains of bacteria and therefore may require different reaction conditions.
An enzyme that recognizes the same sequence but cuts it differently is a neoschizomer. Neoschizomers are a specific type (subset) of Isoschizomers. For example, Sma I (CCC/GGG) and Xma I (C/CCGGG) are neoschizomers of each other.
An enzyme that recognizes slightly different sequence, but produces the same ends is a isocaudomer.
In some cases, only one out of a pair of isoschizomers can recognize both the methylated as well as unmethylated forms of restriction sites. In contrast, the other restriction enzyme can recognize only the unmethylated form of the restriction site. This property of some isoschizomers allows identification of methylation state of the restriction site while isolating it from a bacterial strain. For example, the restriction enzymes HpaII & MspI are isoschizomers, as they both recognize the sequence 5'-CCGG-3' when it is unmethylated. But when the second C of the sequence is methylated, only MspI can recognize both the forms while HpaII cannot.
"Isoschizomers at New England Biolabs". http://www.neb.com/nebecomm/tech_reference/restriction_enzymes/isoschizomers.asp?.