I often come across statements similar to the two below, which make sense in isolation but contradict each other when seen together:

 

1. We share 50% of our genes with a full sibling.

2. We share 90% of our genes with mice (or similar numbers for other species).

 

There's obviously some distinction in definition not being revealed here - could someone explain it to me?

You share 50% of your sequences (ignoring mutations) with you sibling. All of them, down to the naked sequence level.

The second sentence only refers to genes (i.e. genetic loci that are actually transcribed). Also note that it is not meant that the sequences are absolutely identical, base by base, (even within a species we have allelic variations), but that the sequence similarity is high enough to be sure that these genes are functionally (more or less) the same.

So again, the first one goes down to the sequence level, the second only to the gene level.

Also I am pretty sure that the similarity on the gene level between human and mice is somewhere closer to 97% (with both being mammals and such).

You share 50% of your genes with a sibling, but 90% of your species' gene pool with mice.