If I were to remove the "which is" or "that is" from an adjective clause, which type of adjective phrase is formed? [duplicate]

All of these participial usages are examples, as you suggested, of a syntactic rule that deletes a subject relative pronoun and an auxiliary be from a relative clause.

The rule is called Whiz-Deletion. The name is a mnemonic.
The Wh- part of Whiz-Deletion comes from the fact that relative pronouns start with wh-.
The -iz part of Whiz-Deletion comes from the fact that the most common form of be is is.
The "Deletion" part of Whiz-Deletion means that these are the parts that are deleted.

Whiz-Deletion is the source of virtually all post-nominal adjectival phrases, like

• the man in the Moon <== the man who is/was in the Moon
• a boy eleven years old <== a boy who is/was eleven years old
• a policeman standing on the corner <== a policeman who is/was standing on the corner
• a locket found in his possession <== a locket which was found in his possession

Since the purpose of an auxiliary be is to carry the tense, when the be gets deleted, so does the tense; these are tenseless, or "non-finite" -- tensed clauses are "finite". That's why I used "is/was" in the examples above -- there's no way to tell which it should be, except in the last example.

It is, brace yourself, a past-participial verbal. It's a verb phase that functions as an adjective. It's equivalent to the phrase that would be made by adding "which is" or "that is", but it's not an abbreviation.