There are so many different types of seeds - sunflower, canary, millet, rye, safflower, and many more. Each has its own different aid in helping your bird have total nutrition. Some seeds should be fed only on occasion, others each day, and some when your parrot has specific needs. If your bird may present particular health issues (eg. overweight, underweight) understanding each seed's function in your bird's nutrition is going to be of prime value.
French (White) Millet
French (white) millet, commonly fed to budgerigars, is not even needed in a bird's diet. In fact, keep it out if you must, but an occasional handful won't pose any threat to your companion parrot. White millet is a hard seed, that's indigestible, especially to parents feeding youngsters, or youngsters just being weaned. You don't need it, so don't feed it, unless as a treat. The only thing to remember, as a warning, is that this seed should not be fed to young birds, or parents feeding young. It can cause a build up in the crop and intestines, or a rupture in the crop. It can also cause baby birds to choke to death.
Having mentioned the drawbacks of white millet, it should be mentioned that, in the case of an overwheight bird, white millet is especially useful. It can reduce the amount of fat in an overweight bird, if fed for a short time. White millet, along with other millets, are a second-class protein. Overfeeding of high quality proteins leads to overweight. Feeding a lower class protein for a short time, will help your bird lose weight.
White millet is a light brown to creamish color. It is a budgie seed which you have probably encountered. If you pick up a budgerigar seed mix at your local pet store, the majority of it would be White millet.
Niger or Nyjer
This seed is high in protein, and so should be used occasionally, preferrably as a treat only. A small inclusion of this seed in a parrot's diet is not harmful, but could only be beneficial. Just make sure your bird is not picking out these seeds above the others. That's why mixing your own seeds is so important in gaining a nutritionally healthy diet. Too much Niger seed can cause kidney disease.
It resembles small grains of wild rice and has a high fat and protein content. Niger is also known as thistle. Many people think they will be growing thistle weeds in their yard if they offer this seed. In fact, Niger is not a thistle at all. It's the seed of the Niger plant native to Ethiopia. Niger seed sold as birdseed is heated to prevent it from germinating. From: WildBirds.com
Safflower
I see that this seed is a big favorite among companion parrots. It is also very high in protein and so should only be fed in small quantities to prevent your parrot from gaining too much weight. If fed too much, Safflower poses a danger of kidney disease. If given the choice, however, Kiki will eat only Safflower seeds all day. Make sure you provide only a small amount of Safflower to your bird each day, so that if your parrot decides to pick these seeds out, there won't be enough. Safflower seeds are white, a fraction larger than half the size of a Sunflower seed.
Hulled Oats
Another seed that should be fed only in small quantities, as of the threat to kidney disease. This seed is also high in fat and too much can cause a bird to quickly gain excessive weight. I have found that parrots do not like this seed very much and it's always part of the 'leftovers'. This may be individual preference, and some birds may relish it, so keep an eye out on how your bird reacts to this seed. Hulled oats are the light brown seeds, almost as large as a Sunflower seed, but quite a bit thinner.
Rape
This seed is a small, dark, grey-reddish-brown seed. It is a fraction smaller than White millet (budgie seed). It should only be fed in small quantities due to the risk of overweight and kidney disease. It can also be fed as a treat as long as the owner keeps a watchful eye on how much the bird consumes.