the Miracle grow "powder" is what is called a water soluble
plant food. This is good to use on
seedlings because you can give them low doses by sub irrigation. And you CAN burn your
plants up easy if you mix a higher rate then what is recommended.
The tiny beads are CRF, control released fertilizer. It is similar to Osmacote. They are best incorporated into the soil, so that all sides of the beads have contact with the soil. Also if your pot falls over your fertilizer does not spill out.
Once the fertilizer has been applied, the water will fill the beads fill up with and slowly release fertilizers consistently. There are differing release times on different products, anywhere from 3-12 months.
Me personally, I like the Nutricote brand the best for CRF. It is also sold under the brand name Dynamite. It is a gray colored bead or pearl as they are called in the nursery industry.
I could go on and on about this subject but wanted to keep it short....