Does all pistachio flavored ice cream have nut fragments?

Well the cheaper stuff is just vanilla ice cream with green food colouring and almond extract, pistachios have no real strong flavour, the more premium types like B&R or Haagen Daz or even Ben and Jerrys would have real nut pieces and pistachio paste in the ice cream base, pistachio paste is like peanut butter made from mashed pistachio nuts, it adds a bit of flavour, I made real pistachio ice cream and Italian style gelato this way when I was a chef.

Often the lesser brands use chips of almonds not pistachios.

Not if you make it yourself. What I did is ground the pistachios to nut butter (it takes a lot more work than peanuts or almonds), then made a standard custard and put them in the blender together to achieve smoothness, then strained out any bits. It was a bright brownish green. You can also chop and soak the nuts in the milk a couple hours, then proceed with the custard, stick it all in the blender, then strain out the nuts.

Make it yourself at home and you can have it EXACTLY how you want it.

The green comes from food coloring, BTW.