利奇（G. Leech)等人认为，一般说来，补足语这一术语是指必需用来使一语法结构完整的某种成分。他们把补足语分为形容词补足语（adjective complement），介词补足语（prepositional complement)和分句补足语（clause complement)。

形容词补足语（adjective complement):在传统语法中没有形容词补足语这一术语，通常把它分析为状语。某些现代英语语法著作认为，某些形容词和分词形容词（participial adjective）可以要求不同补足语。例如：

1. I'm very glad to meet you.（带to不定式作补足语）

2. l feel sure that you will be all right.（that分句作补足语）

3. Was he successful in his business?/We were all annoyed at his behavior.（介词词组作补足语）

Complement:More widely,any element needed to 'complete' an adjective,preposition,verb,or noun.Complements of adjectives include preposional phrases,e.g. fond of chocolate,to-infinitive(clause),e.g. sorry to hear your news, and clauses,e.g. sorry that you're ill.

Complementation:The addition of a complement to a linguistic unit.For most linguists this is a syntactic concept,but note the semantic perspective in the quotation below:

1985 R. Ouirk et al. We reserve the term complementation(as distinct from complement) for the function of a part of a phrase or clause which follows a word,and completes the specification of a meaning relationship which that word implies.

首先，句意是根本，语法分析要退而其次。无论传统语法还是现代语法，我觉得，只要能对某一语言现象做出合理的解释，就是好语法。语法术语问题，还是建议阅读专业语法书籍。至于如何辨别，主要是对语法知识的领悟问题。学习了语法规则，对于句子的分析理解，除了不断地实践和总结以外，最根本地，就是自己的悟性。个人的一点看法，仅供参考吧。

【1】Mr. Steve【主语】//  is 【系动词】// very easy【表语】//  on his children【对象状语】// .

参考译文:史蒂夫先生对他的孩子们很宽容。

备注:在传统语法里,on his children为介词短语作对像状语。

【2】Mr. Steve【主语】//  is 【系动词】// very easy【表语】//  on his children【补足语】// .

参考译文:史蒂夫先生对他的孩子们很宽容。

备注:在现代语法里,on his children为介词短语作形容词补足语。

介词短语作形容词补足语属于“现代语法里”的语法术语/语法称呼。类似于“传统语法里”的“对象状语/原因状语”。类似于:传统语法把系动词be(am/is/are)后面的内容称作为表语，现代语法把系动词be后面内容称作为“主语补足语”。虽然称呼和叫法不同但是本质是相同的。

以上个人理解,仅供参考。