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.