The most commonly used abstract model for pattern recognition is the classification model. The transducer senses the input and converts it into a form suitable for machine processing. The feature extractor extracts presumably relevant information from the input data. Finally, the classifier uses this information to assign the input data to one of a finite number of categories.
From a theoretical viewpoint, the line between the feature extractor and the classifier is arbitrary. An ideal feature extractor would make the job of the classifier trivial, and a perfect classifier would need no feature extractor.
The problem of feature extraction is much more problem dependent than the problem of classification. The classification is made by partitioning the feature space into regions.
Ideally, none of the classifier's decisions should ever be wrong. In real world problems, where perfection is not always possible, you try to minimize the probability of error.