Score - When an item is just labeled as a "score" in its description than it will generally be a full/complete score. This means that all parts will be written out in full. This is generally what is used by a conductor or for instrumentation analysis purposes.
Vocal Score - A type of reduced score for vocal music. The instrumental accompaniment is reduced to be playable by a single piano, but all voice parts are still present. Generally used by vocalists in rehearsals.
Miniature score - Also sometimes called a study or pocket score. Sometimes the physical item itself is small enough to unobtrusively take to a performance. For more contemporary scores a miniature score often means that the item is still large but the print is small enough that it's generally only good for study, rather than performance, purposes.
Closed score - Least common type of score. A score for wind band (generally) that has been reduced to 4 or 5 simultaneous staves. Does not provide full detail of what every instrument is playing at any given time, but gives a sense of dynamics, rhythm, and harmonic structure.
Parts - The music for each instrument is printed on a separate piece of paper so that one can only see that particular part at once. These are used for performance purposes. Often will be part of a set "score and parts."
Searching for sheet music can sometimes be more complex than searching for books. The following pages have been written to help you locate the piece you want in the exact score format you want.