I think the biopsy you had is a core needle biopsy.

A less invasive procedure is called FNA: fine needle aspiration, that is for a cytology examination, not true histology examination.

An open biopsy is when the surgoen cut on your breast to open it up, and then get some tissue from the lesion. Usually it is larger piece of tissue than core needle biopsy, so more histology information can be obtained from open biopsy.