On a nuclear scintascan, how is arthritis, inflammation and osteoporosis shown, are they in different grey scales?

Bone scans: Don't provide information about bone mineralization. Osteoporosis is determined with a different study entirely, the bone mineral density scan. Arthritis and inflammation show up as areas of increased (black) activity on bone scan.

Depends on settings: Images can either be positive or negative, just like camera film (used) to be. Now, we can even use different color scales. However, active arthritis, increased blood flow, bone fractures and infection all "take up" more of the radiopharmaceutical during a bone scan, and therefore are more radioactive, or more intense/brighter on the image. The areas outside the body have no intensity.

Inflam=more uptake: Areas of increased blood flow and inflammation with cause more uptake in that area on a bone scan. So if someone has an inflammatory arthritis, we would look for increased uptake along both sides of a joint. Bone scintigraphy is not good to evaluate osteoporosis. You would need a DEXA scan for that.