I can absolutely make this distinction. There is a gigantic qualitative difference between continuous small picks where you don't feel the injection and a jab. With a syringe you get upwards of 0.5 mL injected into your body. The syringe has a real size to it. It takes half a minute to get a vaccine and needle is in your arm for more than 3 seconds easily. The entire content of the syringe is injected at one.
My sister has a fear of needles but has tattoos; She does not fear the tattoo gun. This is the case for a lot of people. Your logic blasts past reality.
I also didn't say it was the case for every antivaxxer that they're rationalising a fear of needles. I am explaining one cause of something that knows an innumerable amount of causes.