In extension to shigeta's answer, I could well imagine "tool strains" and "recombinase strains" to be equivalent in the sense that they mean strains of mice whose genome you can easily manipulate.
Cre recombinase is an enzyme which can recombine (effectively insert) genes from a plasmid (which you somehow delivered to the cell) into the cell's genome, if Lox-sites are present (Cre-Lox recombination). This is a very common method of integrating genes into eukaryotic model organisms (i.e. mice).
By tool/recombinase strains they could simply mean mice which express recombinase already, so that you can readily insert your genes into specific cells by delivering a plasmid with the genes on it, and then triggering Cre recombinase in the cells you want to modify in order to integrate the genes into those cells' genome.