The blender, as you have probably experienced, totally pulverizes your ingredients. This can be useful if you need a very finely chopped product — often this means chopped nuts, or herbs, or a fine paste. Or smoothing out chunky soups and sauces. Add liquid to the blender jar, and it incorporates a lot of air. As the liquids combine with solids and get sucked into the blade/blender vortex, air is mixed in. This is great for smoothies and some batters. But not so great for everything. A blender can’t handle a really heavy mix (bread, cookies, sausage) and will burn itself out trying.
The food processor, especially a heavy duty one, is great for chopping. Variable settings on some models mean you can quickly chop or slice veggies, onions, herbs, nuts, and more. Some recipes recommend that you use a food processor rather than a mixer for cakes, cookies, breads and other baked goods. The food processor in general does not incorporate air into the mix.
The stand mixer, with the paddle attachment, is roughly approximate to the food processor — when it comes to mixing. The paddle attachment, especially if it offers planetary motion, will do a thorough job of incorporating most ingredients . Lower speeds mean less air. Higher speeds at longer times mean more air is incorporated. When you’re looking for the lightest, fluffiest mix possible, your choice will be stand mixer with whisk attachment. Or whisking by hand, which some people swear by.
Bottom line, they’re not interchangeable. If a recipe says ‘use a blender’, and you’ve got one, use it.