What is the relation between 寨 (zhài, "stockade, stronghold, fort") and 塞 (sài, "place of strategic importance; pass; fortress")?
There doesn't seem to be much relation between「寨」and「塞」, although it takes some evidence to demonstrate why this is the case.



Firstly, the reason why many dictionaries say that「寨」is「塞」plus「木」is because「塞」is popularly but very likely mistakenly interpreted as the modern character for what was originally「賽」. The evolution of「賽」from oracle bone script to modern form is considered by some paleographers to be the following:



Basically, what appears as「工」in this character (and some others) is considered by several experts as a simplified form of「玉」, and sometimes was written as「玉」, while the two hands「廾」were sometimes removed in certain variants and「貝」was sometimes added as a semantic indicator. The character was a compound ideogram depicting the offering of objects to spirits inside a temple, and the primary meaning was to do with some kind of ritual, preserved in the ancient words「賽神」and「祭賽」.

As stated near the beginning, many important sources however say that the first two forms is the ancient form of「塞」(plug, fill in). For example:


  段玉裁注：“凡填塞字皆當作。”


(「」is the second form in the evolution sequence depicted above. With a bit of stroke joining and simplification, 「」becomes「」, which is the top part of「賽」and the other characters mentioned in this question.)

Note that these sources, although traditionally very well reputed, do not appear to provide any paleographic or lexical evidence for this assertion, and so cannot be trusted for this specific character. Despite this, many dictionaries will follow these sources and treat「」as the original character for「塞」, and subsequently interpret「寨」as「」(mistakenly thought as 塞) plus「木」.



Interpreting the primary meaning of「賽」as a religious ritual, it is then very likely that「寨」and「塞」merely use「」(賽) as a phonetic component.


「塞」uses「土」as a semantic component to indicate the meaning stuff, plug, fill in. This is an ancient definition that has survived very well intact to the present. Note that the synonym「填」uses the same semantic component.
「寨」is only one possible form of the word it represents, the other commonly seen one being「砦」.
The only time when the two characters have anything to do with each other is for the meaning fortification.




Further reading:


季旭昇《說文新證》
于省吾《甲骨文字釋林》
何琳儀《戰國古文字典》




Please note that this explanation is tentative, and there will undoubtedly be differing opinions on these characters. More evidence is required to make a more solid case.