What is the difference between ovarian cysts, tumors and cancer?

Lot of difference. Cyst are benign lesions containing fluid inside, cystocarcinomas also contain fluid inside are cancers which need to be differentiate from benign cyst, by test, by removal & microscopic examination. Some malignant tumors are solid not cystic. Go to your gynecologist.
Related. Cyst is a fluid filled structure; ovarian cysts may be just that; but cysts in the ovary can be benign or cancerous tumors. Ovarian tumors, benign or malignant, may be sold or cystic. So, these are all related to each other and sometimes difficult to differentiate.