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Are Stars and Bars in Combinatorics related to the Fence Post Error?

The bars in the lower picture look like fences. That's why Stars and Bars reminds me of [Fence Post Error](https://en.wikipedia.org/wiki/Off-by-one_error#Fencepost_error)?

>It is common to replace the balls with “stars”, and to call the separators “bars”, yielding the popular name of the technique. We have 5 stars, and 2 bars in our example:

>![](https://www.themathdoctors.org/wp-content/uploads/2018/12/Stars-n-bars-apple-1c.png)

Above's [Source](https://www.themathdoctors.org/stars-and-bars-counting-ways-to-distribute-items/). 

>![](https://i.imgur.com/X6In8o2.jpg)

Blitzstein. *Introduction to Probability* (2019 2 ed). p. 19.