I want to give a practical guide to vector illustration for artists coming from a raster painting background, because the transition requires a significant mental model shift.

The fundamental difference: in raster you build up pixels. In vector you define mathematical shapes. The shapes can be scaled infinitely without quality loss. Raster work looks perfect at its native resolution and degrades with scaling.

When to choose vector: logos, icons, illustrations intended for multiple output sizes, any work that needs to scale from a business card to a billboard. Vector is the right tool when scalability is a requirement.

When to choose raster: complex painterly work, photo manipulation, anything with subtle color gradations and textures. Raster is the right tool when complexity of visual information is a requirement.

The entry point for raster artists: Adobe Illustrator's pen tool is the standard, but it's unintuitive. Affinity Designer's pen tool is more learnable with a raster background. I recommend starting with Affinity Designer. The concepts transfer to Illustrator once you understand them.