Osteogenic sarcoma and osteosarcoma are the same tumors?

Yes. The two are synonyms. By definition, it is a sarcoma that produces malignant osteoid (immature bone) that is seen under the microsope. Osteogenic means "producing bone." other bone sarcomas, like ewing's, do not produce osteoid. Most arise in bone, but there are rare soft tissue osteosarcomas (or osteogenic sarcomas, depending on which term you prefer).
Yes. Yes. Osteogenic sarcoma is often shortened to osteosarcoma.