To answer your question precisely, core samples of mass or tumor are obtained using a core needle (hollow needle) for diagnosis.
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In the 'needle core biopsies" generally, a large bore needle is used and the operator, mostly a pathologist (medically trained) will feel the lump or lesion, hold it between his fingers and push the needle through the numb skin several times to get pieces of tissues and cells and then spread them out on a slide, or create "cell blocks" that re-capitulates the original tissues, this is a CYTOLOGICAL technique.
In the "tissue core biopsies", a special designed large bore cutting needle is used to get to deeper lumps not felt by the hand, but rather seen on ultrasound,and using a device that locates it, the trucut needle goes in and cuts out a piece of the tissue in the form of a cylinder (resembling the bore of the large needle), these are actual tissue samples and not cells, fragments or fine particulate matter from the lump. The tissue is processed as such and read as biopsies as done in HISTOLOGY as compared to the previous methodology called cytology.
The second METHOD of core biopsy is much more accurate, as it provides the tissue and the entire configuration of the lesion (cancer, adenoma, etc) within the tissue matrix. One can check online resources to see papers published on this topic.