What's the difference between HEAD^ and HEAD~ in Git?

Question

When I specify an ancestor commit object in Git, I\'m confused between HEAD^ and HEAD~.

Both have a \"numbered\" version like HEAD^3<

Answer 1

Simply put, for the first level of parentage (ancestry, inheritance, lineage, etc.) HEAD^ and HEAD~ both point to the same commit, which is (located) one parent above the HEAD (commit).

Furthermore, HEAD^ = HEAD^1 = HEAD~ = HEAD~1. But HEAD^^ != HEAD^2 != HEAD~2. Yet HEAD^^ = HEAD~2. Read on.

Beyond the first level of parentage, things get trickier, especially if the working branch/master branch has had merges (from other branches). There is also the matter of syntax with the caret, HEAD^^ = HEAD~2 (they're equivalent) BUT HEAD^^ != HEAD^2 (they're two different things entirely).

Each/the caret refers to the HEAD's first parent, which is why carets stringed together are equivalent to tilde expressions, because they refer to the first parent's (first parent's) first parents, etc., etc. based strictly on the number on connected carets or on the number following the tilde (either way, they both mean the same thing), i.e. stay with the first parent and go up x generations.

HEAD~2 (or HEAD^^) refers to the commit that is two levels of ancestry up/above the current commit (the HEAD) in the hierarchy, meaning the HEAD's grandparent commit.

HEAD^2, on the other hand, refers NOT to the first parent's second parent's commit, but simply to the second parent's commit. That is because the caret means the parent of the commit, and the number following signifies which/what parent commit is referred to (the first parent, in the case when the caret is not followed by a number [because it is shorthand for the number being 1, meaning the first parent]). Unlike the caret, the number that follows afterwards does not imply another level of hierarchy upwards, but rather it implies how many levels sideways, into the hierarchy, one needs to go find the correct parent (commit). Unlike the number in a tilde expression, it is only one parent up in the hierarchy, regardless of the number (immediately) proceeding the caret. Instead of upward, the caret's trailing number counts sideways for parents across the hierarchy [at a level of parents upwards that is equivalent to the number of consecutive carets].

So HEAD^3 is equal to the third parent of the HEAD commit (NOT the great-grandparent, which is what HEAD^^^ AND HEAD~3 would be...).