Homozygous SNPs are the ones where both homologous chromosomes of the non-reference genome have the same allele and different from the reference genome. For mouse, most of the strains are inbred ( i.e. they have same allele for both the homologous chromosomes OR both the parents have contributed the same allele). So, if you compare a non-reference mouse to a reference mouse strain and if there is a SNP on one of the homologous chromosome then the same SNP will appear on the other homologous chromosome if the non-reference strain is inbred.
But in case of human, both father and mother can contribute different alleles and when you compare it with the reference allele, then it may be a case that the father's allele differ from the reference one but the mother's allele are same as that of reference. In this case, both homologous chromosomes have different alleles and one matches the reference and one does not. This will be an example of heterozygous SNP.
Hope it explains. Please feel free to ask questions.
Edit to include a drawing
AAATTTGGGCTTTAAA - Reference genome (Chr 1)
AAATTTGGGtTTTAAA - Non-reference genome (Chr 1 from father)
AAATTTGGGtTTTAAA - Non-reference genome (Chr 1 from mother)
Above is an example of Homozygous SNP ( t replaces C on both the Chr 1)
AAATTTGGGCTTTAAA - Reference genome (Chr 1)
AAATTTGGGtTTTAAA - Non-reference genome (Chr 1 from father)
AAATTTGGGCTTTAAA - Non-reference genome (Chr 1 from mother)
Above is an example of Heterozygous SNP ( t replaces C in father but not in mother)
If you're "well aware" of the concepts of homo- and heterozygous, then it's unclear where your question actually arises. Regarding actually calling these variations, have you read any of the papers on SNP callers? BTW, all variation can be heterozygous, in most cases it's just unlikely for them all to be heterozygous at the same time.
Ok, I understand the need of this question for myself so I thought of asking it here !! Sorry, If it was not clear for you. Yes, I read some paper on SNP calling but I was not asking about SNP calling too.