"Pikey" refers to Irish Travelers. They're ethnically Irish, they're white. It's a culture, not an ethnic group.
Gypsy refers to the Roma, and some other Romany ethnic groups, such as Sinti. It refers to an ethnic group, with its own distinct culture. But it's primarily an ethnicity. If you're a Gypsy, you're a Gypsy regardless of whether or not you travel, which is why a lot of Gypsies don't identify as "traveling folk," many Gypsies don't live a traveling lifestyle anymore, and those who do, it's often due to forced deportation rather than a lifestyle choice. I'm a Roma Gypsy, and my family hasn't traveled since moving to the US 3 generations ago.
So bigotry against Gypsies (which is referred to as antiziganism) is a form of racism, bigotry against Travelers is still wrong, but it's bigotry, not necessarily racism.