Can I freely apply for visa-free Schengen countries after European immigration?

For those who apply for European immigration, one of the benefits is to obtain the "Schengen country residence status". Having a visa or residency in any Schengen member country is equivalent to having a "European Pass" and being free to enter and leave 28 Schengen countries.

However, it should be noted that not all European countries are Schengen countries, such as Britain, Ireland and Cyprus.