You have the right idea. Redworms will help your growbeds. But worms that are red colored are not necessarily redworms. Using worms you find in your soil is not necessarily bad. What you may have there is some redworms. 'Redworms' is not actually a species of worm, it is more like a class of worm just like there are classes (or groups ) of dogs, such as working dogs, companion dogs, hunting dogs, etc...Generally, redworms are found in the upper soil horizon composed completely or heavily of organic matter that is being broken down. Redworms do not live in a pure soil environment. That is the realm of what you are calling "earth worms". Earth worms require soil for their survival. Redworms require deteriorating organic matter for their survival. Most likely the "earth worm" you put in the growbeds will not survive, or will attempt to leave, if possible. The smaller ones might be truly redworms, but there are many many speices of worms, and many species of redworms. Some redworms are better suited for life in growbeds. Some redworms are better suited for outdoor growbeds. Knowing what species of redworm you are dealing with helps match the specific worm to the task you wish to accomplish. Some redworms have a wandering habit and are not suited for life in a growbed or composting bin, yet will work well in a large outdoor compost pile. Eisenia fetida (scientific name) is the most commonly used redworm for bin composting and aquaponics, because it is tolerant of a wide range of living conditions, reproduces rapidly and does not have a wandering habit.
If you are comfortable giving the worms you found a try, I say go for it! It will not actually hurt anything. If you want to be sure you are getting worms that are certain to fit the task you want accomplished, in the place you want it accomplished, then you might want to buy some redworms. If you go to your local "worm ranch' just be sure the people there can tell you exactly what species of worms they have (by scientific name - common names are used indiscriminately and interchangeably among those who do not know better)...otherwise you may be better off just digging them up yourself.
Hope this is helpful. If you have any more questions, please let me know. We operate a commercial scale redworm farm, and are pleased to help fellow aquaponics enthusiasts when we can.