In "New Practical Chinese Reader 2", it introduces two complements for
Chinese verbs, in two different chapters. The first one being,
complement of state, like 他跑得好。(He runs well)
The second one being, the resultative complement, like "记错". (to
I think the first type of complement if more commonly called a "complement of degree," but either term could work.
Complements of state/degree can be used in only one structure "verb + 得 + complement." Resultative complements can be used in three structures: 1. " verb + complement"; 2. "verb + 得 + complement"; and 3. "verb + 不 + complement." There is only overlap if the complement takes the form in 2.
In the structure "verb + 得 + complement," there is no automatic way to know which structure is represented, but generally it is still clear, since most words cannot be used in both structures. Any Chinese "adjective" indicating a quality or degree can be used as a "complement of state/degree"; however, the set of words that can be used as a resultative complement is more limited. Also, the meaning of the structures is similar, but different.
For example, a negative word can be used as complement of state/degree, but not as a resultative complement. Because of this difference, if you ever see the sequence 得不, you are dealing with a complement of state/degree. An example is the sentence: 儿子每天的练习都做得不对. The phrase 不对 must be a complement of state/degree and the sentence must mean that manner of doing the exercises ended up wrong. Technically, this does not actually assert that the result itself was wrong, since you can use an incorrect procedure and still end up with a correct result. English would have the same technical ambiguity, but pragmatically, if you say, he did the exercises wrong, you are usually talking about the results and not just the procedure. The Chinese is the same.
This sentence has structure number 1. above, and so we must be dealing with a resultative complement. Technically, this does not assert that the procedure was correct, only that the result was correct. Pragmatically, in both Chinese and English, such sentences are used to indicate both things.
For example, what's the difference between these two sentences:
（包:to wrap a parcel)
a) 请包好。 b) 请包得好。
Sentence a) uses the structure in number 1. above and so must have a resultative complement. The second uses structure number 2. and so is formally ambiguous. I don't think, however, that either usage of 得 is compatible with an imperative.
The expression 包好 is not used to mean that the wrapping should be "nice," but rather that the wrapping should be secure. When used as a resultative complement 好 indicates that the expected state of success is reached. Used with 包, 好 can be translated as "well" but means "securely."
Used alone, 包得好 is okay to use with a resultative complement to mean "can wrap so as to be secure." In theory, it could also be used with a complement of state/degree to mean "wrap so as to end up with a nice result; however, I do not think such a usage is usual in the face of the existence of the resultative complement. If you had to express this meaning of degree, you could also say 包得很好. A resultative complement can never include an adverb like 很, and so the presence of 很 disambiguates what follows as a complement of state/degree.
Are these two complements interchangeable? Or is there any difference
between these two complements?
As I have described, generally a word or phrase is used only with one structure or the other, even if there are only small differences. In the few cases were both can be used, you can use 很 to disambiguate them, since without it, the resultative complement is generally the default meaning.
The difference in meaning is that the resultative complement describes the final state created by an action, whereas the complement of state/degree describes an assessment of the degree reached by the action itself. The former does not actually tell you anything about the manner or degree of the action. The latter does not actually tell what final state is reached, just the manner or degree to which the preceding action was carried out to reach the state.