The general equation of a circle radius a is (x-b)^2+(y-c)^2=a^2, and the centre is at (b,c). Completing the square, y^2-2y+1=(y-1)^2=20. There is no x term so b=0 while c=1. The centre is at (0,1).
The second circle equation can be written (x+1)^2+(y-2)^2-6=0 because x^2+2x+1+y^2-4y+4-6=x^2+y^2+2x-4y-1=0. So the centre of the second circle is at (-1,2). The y difference between the two centres is 2-1=1 while the difference between the x values is 1, so the difference between the centres is sqrt(1^2+1^2)=sqrt(2).