Um... You provided your own answer. The "high profile" cases are a subset of all "hate crimes" (and are presumably large scale type events).
I said "high profile", because those are the ones that we know about.
And? The high profile ones tend to also be the ones that had the broadest impact, and thus are more likely to be known. Thus, they're inherently more likely to share many of the features associated with terrorism. That in no way means that all hate crimes are terrorism, which, if you recall, was the point I was questioning.
For it to be terrorism, there has to be an intent to use the event to put fear into the population as a whole
Knowing that you would could be assaulted for simply existing is placing fear into the population as a whole.
No. It puts fear into you. If the aspect of your existence that it targeted is shared by a group, then it puts fear into that group. That's not the same as the population as a whole. If I plant bombs in random places where people congregate and set them off to randomly kill whomever happens to be there at the time, then everyone is at risk, and everyone is fearful. If I hate left handed red headed step children, and engage in targeted attacks against that set of people, then the only people who are afraid are those in the group.
The former case is terrorism (well, most likely). The latter is hate. While they can overlap, they are not the same.
with an eye towards changing positions/policies in some way
Hence why I said in a meaningful difference. To the people being assaulted, it's all the same. I understand the textbook difference, but there are negligible differences on the actions, especially to the victims.
Again though, that's the point. The objective of terrorism is to put fear into everyone, not just the victims of the attack, or those who share some criteria with those victims. That is, arguably, the defining characteristic of terrorism. It's not targeted at a single group. It's specifically designed to make everyone take the terrorist seriously because anyone
could be killed.
The IRA planted bombs in public places and then called up the cops and told them where the bombs were. In most cases, no one was injured (with some notable exceptions).
I replied to your quote "Not all hate crimes are terrorism". Your example is that not all terrorism is a hate crime. Unless you were to argue the absence of love in the said terrorist action, I would agree.
I gave two examples. One showing how hate crimes don't always meet the criteria to be terrorism, and another showing how terrorism doesn't always meet the criteria to be a hate crime. You've chosen to ignore the first one. I'll repeat it for you:
Some guy randomly beating up a gay guy because of his sexual orientation is committing a hate crime. He's not even remotely committing an act of terrorism though. Somewhat by definition a hate crime is the result of someone's hate (obvious yeah). If you hate <insert group here> you're not necessarily planning some grand scheme to influence people's opinions much less broad political policies when you take a hateful action towards a member of that group. The thought process for such people likely does not extend much beyond "there's someone in <insert group> right there! Let's get him!"