What''s the difference?

Far as I've figured, it's just 2 different names for the same thing. Although as veg gardeners we should really feed the soil rather than the plant, most of us tend to feed the plants, particularly with 'side dressings' of feed.
Fertilizer is generally thrown onto the soil and worked in. Plant feed can be dressed around the plant in whatever form it comes in (liquid, granules, powder) or it can be thrown onto the soil. Rather depends on what it's really for - general health, specific growth problem, etc.