Actually, the use strict pragma and the package statement are not that different.

use strict;
# strict is on.
{
   no strict;
   # strict is off
}
# strict is on.
[download]

package Foo;
# Currently in package Foo.
{
   package Bar;
   # Currently in package Bar.
}
# Currently in package Foo.
[download]

You can't have two current packages at the same time, just like you can't have two strict states at the same time.