Conization may be performed using a surgical knife (cold knife cutting, or CKC), by C02 laser, or by LEEP. The goal of conization is to remove both surface and underlying tissue damage from CIN so that only healthy cervical tissue remains.
When it comes to diagnosis, cone biopsy is not the standard form of biopsy during a follow-up visit for abnormal Pap smear results. More commonly, if a doctor decides that a biopsy is necessary during a colposcopy, a punch biopsy is taken instead.
A punch biopsy removes a much smaller piece of tissue than a cone biopsy and therefore has a shorter healing time. On the other hand, a cone biopsy incorporates built in therapy, while individuals with a positive punch biopsy will need to return for treatment at a later date.
In the end, the important thing to remember is that many physicians use the terms "cone biopsy" and "conization" interchangeably. Since any treatment procedure can also be used for diagnosis, and vice versa, that's perfectly understandable -- it's just confusing.
Kim JH et al. (2009) "The role of loop electrosurgical excisional procedure in the management of adenocarcinoma in situ of the uterine cervix." Eur J Obstet Gynecol Reprod Biol. 145(1):100-3.