Fibroadenoma: This is a common benign breast tumor, especially in young women. They are typically painless, movable, and have a firm, rubbery texture, which matches the description provided.

Cyst: Breast cysts are fluid-filled sacs within the breast and are very common. They can be movable and are often painless, although they may cause discomfort during certain times of the menstrual cycle.
Lipoma: A lipoma is a benign tumor made up of fat tissue. It can occur in the breast and is usually painless and movable.
Hamartoma: A hamartoma is a benign growth that can occur in the breast. It is composed of a mixture of tissues normally found in the breast and can be movable and painless.

Phyllodes Tumor: Although most phyllodes tumors are benign, a small percentage can be malignant. They can present as a painless, movable mass, making them a critical diagnosis not to miss due to their potential for malignancy.
Breast Cancer: While breast cancers are often associated with pain, a significant portion can be painless. Given the potentially life-threatening nature of breast cancer, it is crucial to consider it in the differential diagnosis, even if the mass is movable and small.

Pseudoangiomatous Stromal Hyperplasia (PASH): PASH is a rare benign condition of the breast that can form a mass. It is more common in young women and can be movable and painless.
Adenoma: Breast adenomas are rare, benign tumors. They can present as small, movable masses and are usually painless.
Neurofibroma: Although more commonly associated with neurofibromatosis type 1, isolated neurofibromas can occur in the breast. They are benign nerve sheath tumors and can be painless and movable.