I don't think "no true Scotsman" is a separate fallacy from moving the goalposts at all. It's a subcategory: All "No true Scotsman" fallacies are cases of moving the goalposts, but not all instances of moving the goalposts are cases of "no true Scotsman".
In moving the goalposts, the speaker states something that can be falsified by X, and when X is shown to exist, he denies that X is a counterexample by saying that it has to be some special instance of X, or requires X in conjunction with Y, in order to qualify as a falsification.
In "no true Scotsman", the speaker sets up an initial standard, "No Scotsman would do that." Implicitly, such a statement can be falsified with an example of a Scotsman who did or does such a thing. But, when presented with exactly such a counterexample, the speaker denies the counterexample with "No *true* Scotsman would do that". It is moving the goalposts because the original standard for falsification has been modified. (In particular, it has been modified in a vacuous way, since "true" doesn't carry any discernible meaning other than to distinguish Scotsmen who would never do such a thing from Scotsmen who would.)
An example of moving the goalposts that is not "no true Scotsman" would be a Creationist saying, "You can falsify Creationism by showing me an example of an organism that evolves over time." Then, after being shown this video https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjz0qCaxdTSAhULilQKHZd-Du8QyCkIHDAA&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DplVk4NVIUh8&usg=AFQjCNEfeMi-uYyz_H60Jq84bqhbmam2zw&sig2=Vy0VAHrkGsJcjtrdApagMA&bvm=bv.149397726,d.cGc
, demands to be shown an example of a multicellular
organism that evolves over time.