Admittedly it's occasionally difficult to tell apart a 熟語 and a 複合語, and there are different opinions. Here I will explain how I use these terms, based on their "narrow" definitions.
熟語 are rarely coined today, are listed in dictionaries, and may have completely different meanings from their constitutive elements. Although it's possible to analyze a 熟語 etymologically, they are basically established "words", and you have to learn them one by one. For example, unequivocal 熟語 include 鉛筆 ("pencil", 鉛 "lead" + 筆 "brush"), 日本 ("Japan", 日 "sun" + 本 "origin") and 矛盾 ("paradox", 矛 "spear" + 盾 "shield", from this tale). In English, a 熟語 is analogous to words like "helicopter", "peanut", "bracelet" or "hydrogen".
複合語 are straightforward combinations of two or more existing words. They may not be listed in dictionaries, but they still refer to some notable concept that may be worth listing in Wikipedia. Examples include 風力発電 ("wind power"), 携帯電話 ("mobile phone") and 産業革命 ("industrial revolution"). Note that some people think these are also 熟語 just because several kanji are grouped. I personally do not like calling these 熟語 because there is nothing "idiomatic" in them. There are also kana-kanji 複合語 like フランス料理 ("French cuisine") and long 複合語 like 世界自然保護基金 ("World Wide Fund for Nature").
Naturally, 複合語 tends to be longer, and most 熟語 are made of two kanji. But there are longer 熟語 (see yoji-jukugo), too.