What is the difference between an item of clothing and a piece of clothing? Can I say "three pieces of clothing" or "three items of clothing"? Are they used identically?
There is no difference; "piece" and "item" are merely different counters used with clothing. Note that "article" is also used.
So the statements
. . . three pieces of clothing
. . . three items of clothing
. . . three articles of clothing
are functionally the same.
It depends on the situation... Usually, they are interchangeable, but there are cases where this is not so. If, for example, you were talking about a murder:
"These blood-soaked items of clothing...", would refer to complete garments - while "These blood-soaked pieces of clothing..." would be parts of a garment that were ripped or cut off.