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There are six types or classes of cavities which are used daily in dental school and of course in private practice.  It is always good to get exposure to this terminology before school (or as a review).  By your second semester of dental school this should be second nature. I have usd terminology in these definitions that can be reviewed here.
Class I:

Caries involving the pits and fissures on the occlusal, buccal and lingual surfaces of molars (occlusal 2/3 of the crown), the occlusal surfaces of premolars, and the lingual surfaces of incisors and canines.

Class II:

Lesions (another word for an abnormal area) on the proximal surfaces of posterior teeth (premolars and molars).

Class III:

Lesion on the proximal surfaces of canines or incisors which do not include the incisal angles.

Class IV:

Proximal surface lesions that include the incisal angles of incisors and canines.

Class V:

Lesions of the gingival 1/3 of the facial and/or lingual surfaces of all teeth.

Class VI:

Lesions of cusp tips of canines, premolars, or molars or the incisal edges of incisors that do not impinge on the incisal angles.

These are the simplest definitions and because they are basic definitions dental schools like to make them harder by adding information to them.  For example when a tooth is developing caries , the caries will form a triangular shape as it courses through the enamel.  When it reaches dentin a new triangular shaped form will occur.  In a radiograph this decay looks like two triangles stacked with there bases touching (forming a diamond shape).  It is called base to base.  It should be noted that decay has a mind of its own and so not all decay takes this form, but it is just something else you can apply to the basic definition of Class I.  Various classes of cavities have various forms of decay, like apex to apex or apex to base.

It should also be mentioned that when you prep a tooth because it has proximal decay (1st maxillary molar for example - Class II) the preparation is also given the name Class II. If there is caries on the mandibular central incisor but not the incisal angle then the prep would be called a Class III prep which matches the Class III lesion you have surgically removed.

Again this is basic stuff and you are taught it once and are expected to know it from there on out.  I also wouldn’t imagine many schools taking too much time explaining the intricacies of these either.  They show a picture or illustration of a tooth with a black spot on the area that meets the definition and move on to the next slide.  Hope it helps.