Both noun clause and relative (adjective) clause start with a relative pronoun who, whom, whose, which, that.  

Noun Clause

Function: Acts as a noun in the sentence.

It can be a subject, object, subject complement, object of a preposition, or appositive.  

What it does: Names a person, place, thing, or idea.  

How to identify it: Ask yourself if you can replace the clause with a single noun or pronoun. If so, it’s likely a noun clause.

Examples:

What he said surprised me. (subject)

I know that you are right. (object)

The truth is that I was scared. (subject complement)

I’m interested in what you think. (object of a preposition)

Adjective Clause (Relative)

Function: Acts as an adjective to modify a noun or pronoun in the sentence.  

What it does: Provides more information about the noun it modifies.  

How to identify it: It usually starts with a relative pronoun (who, whom, whose, which, that) or a relative adverb (where, when, why).  

Examples:

The book that I borrowed [is] overdue. (modifies “book”)

The woman who lives next door [is] a doctor. (modifies “woman”)

The city where I was born [is] far away. (modifies “city”)