I want to have a summary field, called total_stock that shows a summary of all occourances of a part number in a database. Unfortunately, what it does right now is show totals for ALL part numbers in the group of found records.

basically, if I search by part number it works perfectly, but if I search by some other criteria, say, a PO, it'll display the total of all units in that search.

Try creating a self-relationship based on PartNumber, then make total_stock a calculation field of Sum(relationship::Units). Does this produce the desired result?

Summary fields are useful for reports and are only visibly accurate when the records are sorted by the break field, the fields are contained within a subsummary part, and you are in Preview Mode. They will not work as you might expect, when in Browse Mode.