Also possible to be different car, due to different color (I think, or same color but different lights/smoke???), between that silver or white car and this grey car).
Yes. The Cherokee was popular in japan as an import vehicle and the version there had different tail lenses than the US version. Link to "www.japanpdximports.com"
1987-91 Nissan Y31 Cedric with those tail lamps, and considering how these police cars just look like civilian models with police markings added on, I'm willing to say it could be a Cedric Brougham