Yes the wagtail bird can be all these.But these are only the British and European wagtails and there are many ore wagtails worldwide here is a complete list;

1.White Wagtail(or pied)

2.Japanese Wagtail

3.White-browed Wagtail

4.Mekong Wagtail

5.African Pied Wagtail

6.Citrine Wagtail

7.Yellow Wagtail

8.Grey Wagtail

9.Cape Wagtail

10.Madagascar Wagtail

11.Mountain Wagtail

As you can see from this list there are 11 wagtails world wide including the Grey,yellow and pied wagtails.

Japanese Wagtail was created in 1885.

Forest Wagtail was created in 1789.

White Wagtail was created in 1758.

Mekong Wagtail was created in 2001.