Agree with water daddy, likely not corrosion but rather something settling out. However, are you sure there are no galvanized nipples or section of pipe in the run? Coming from isolated draws rather than whole house would indicate such.
Is the supply well or municipal?

This is a water well, we live in the country. I will ask my H if there are any galv nipples or section of pipe, not exactly sure what you mean by "section of pipe". He is a stickler for perfection, pretty sure everything is on the up and up. But, will ask him anyway. I sure hope you guys can help us figure this out, it is driving us nuts. Thank you both for your time!

"Section of pipe" simply means any piece longer than standard nipple lengths.
Galvanized pipe is still considered an acceptable material in many locales but will suffer from pH. There are parts of the U.S. where acidic water is common.

Does your toilet tank collect the same material?

Any treatment (softener, filtration, ...etc?). Also curious about the answer to laat2's question. Blackish rust sounds like Manganese. This metal can be dissolved into water and is clear until it is oxidized and appear as a color tint or when plated appears as black specks.

I have this issue with my bathtub and toilets, I get little pieces of rust in my tub and our toilets have it in the tank. Also we have to remove our screens on our faucets and clean those out when the water starts to come out slower. Someone came and put a filter in just about a week ago to catch anything that may be coming in from the well, but I am still seeing the specs in the tub and a few now in the toilet tanks again after cleaning all of them out. We built this house, all pipes are the plastic tubing, but the well was here when we bought the land so i don't know what kind of pipe runs into the house. any suggestions?

If your home's plumbing is not metal, then the rust is likely coming from the well pipe and casing. You didn't say how old the well is or how long it's been since you build your house. If the well is old I would pull it now, hoping it may be pulled intact, and inspect the pipe and casing. It may be costly, depending upon the depth of your well, but it will be more costly if you wait until it fails catastrophically.

For right now, do a thorough flush of all of the house plumbing (with faucet screens removed) to see if you can get rid of debris in your pipes.

Thanks for the info, I'm passing this on to my husband

I just remembered that the motor (I'm not good with the terminology for well stuff so bear with me) went out on our well a few years ago and it was pulled and the piping is PVC, I believe that's what it is called, (plastic) so maybe it is the casing, and if I'm not totally off, I believe our well is about 200 feet deep so it was quite a task to pull to replace the motor.