Curators Code wants it to mean this but that's not what it means in my experience.

In practice there is 90% overlap between these terms and both denote the tertiary source you became aware of the link through.

The difference when it exists is that "HT" is less likely to add anything you don't see in the source whereas "via" will sometimes be worth clicking through to see that person's insight.

Hat Tip:

A -> B -> Me

B added nothing, you should visit A for the source. Goodwill link to B, you should check out his site.

Via:

A -> B -> Me

B may have added something. You should visit A for the source and if you have time B might be worth it.

real world examples look like this

Flickr photo (ori) -> example.tumblr.com -> my blog "photo via example.tumblr.com"

Youtube clip (ori) -> John Doe on FB -> your FB "youtube clip via John Doe"

so 'via' is the place where you clicked repost/share not the original content

In practice, I don't think anyone actually has a definitive answer to what differentiates them.

I always interpreted them as mostly meaning the same thing.

I've used via as "from a website" and hat tip as "from a tweet", mostly because I will use "via" on my blog and "ht" on Twitter.

"Via" should not mean the original source because it means "through" or "by means of".

on tumblr, 'via' tends to be how your found it and 'src' tends to be the original post.