I recently embarrassed myself by not knowing the difference between knock-in and transgenic mice, so here’s an explanation to make sure I understand it.
The key difference is that knock-in is targeted, meaning the desired gene is inserted into a specific locus in the target genome via homologous recombination. For instance, in Jackson 2009‘s FFI knock-in mice, the mutant FFI Prnp gene is located in exactly the locus where Prnp is always located in mice. This is important because it means the gene will achieve biological (i.e. natural) expression patterns and levels.
By contrast, transgenic models use random integration: the desired gene could end up anywhere in the host genome. The desired gene might be placed under its own (strong) promoter, leading to high levels of expression, which can be good for disease models, leading to an earlier or more robust phenotype. But the tradeoff is that it’s not as faithful a model of the human disease. One possible issue is that the expression pattern might be all wrong. For instance, Prnp in mice is normally expressed more highly in neurons than in glial cells. If a Prnp transgene were overexpressed in glial cells, that would be ectopic expression and it could lead to a less accurate disease phentoype, and we might have less confidence that therapeutics effective in that mouse model would translate to humans.
In either knock-in or transgenic models, the introduced gene can be be from the same species or a different species. You will find a few web hits defining transgenic as meaning trans-species (e.g. Yahoo! Answers) but that’s not how scientists use the term, and the Wikipedia articles (transgenesis, transgene) and more credible news outlets such as the New York Times are careful to always say the gene comes from “a different organism” or “an unrelated organism” rather than a different species. There is no question that researchers in the prion disease field take the term “transgenic” to include same-species random integration: for instance, Cortes 2012‘s GSS mice are referred to as Tg(PrP-A116V)– that Tg stands for transgenic– same for the Tga20 mice [Fischer 1996] which have elevated copy number of mouse Prnp and thus overexpress, leading to earlier disease onset if infected with scrapie.
Just as transgenesis doesn’t necessarily involve a different species, knock-in doesn’t necessarily imply the gene is from the same species. A search for “knock in human gene in mice” did reveal papers [Chan 2004; Besaratinia 2010] doing knock-in of human genes into mice.