If a woman has a solid mass in breast (not a fluid filled cyst), does this automatically mean it is cancer?

It should be checked: Automatically, no. It could be fibrocystic breast disease, which is not at all dangerous. However, it should not be ignored. Additional imaging, and possibly a biopsy are warranted.

Breast mass: Not all breast masses are cancer. There are also benign conditions such as a fibroadenoma that can be a breast mass. You should see your doctor for further evaluation.