There are two differences.
First, if a cop pulls you over for speeding, it's not for "traveling at an unsafe speed". It's because you were going faster than the posted limit. The law says nothing whatever about such a speed being unsafe. In practice, cops usually don't pull people over just for speeding, but only for going significantly faster than the general flow of traffic. But that's only usually; cops in most jurisdictions have monthly or quarterly ticket quotas, and if it's getting close to the end of the quota period and they're behind on tickets, it's simple to go out to places where people routinely speed and start pulling everyone over. I have seen this happen.
"Driving erratically", unlike "going faster than the posted speed limit", is always a subjective judgment on the cop's part (in most jurisdictions it's something like "reckless driving" or "driving in a clearly unsafe manner"), but the whole point is that it's supposed to be rare; by definition most people on the road will not be driving recklessly and this kind of law can't be abused in the way I described above just to make a ticket quota.
However, the important difference I was talking about was not between speeding and "driving erratically", it was about under what circumstances the cop can write you a ticket that forces you to either pay a fine or come to court. Under our current laws, a cop can do that whenever he pulls you over--there will always be some traffic law you were violating. ("Driving erratically", or something similar, in itself is a traffic violation under current law.) Under the libertarian system I have been describing, the cop could not write you a ticket that forces you to either pay a fine or come to court unless you actually caused harm. He could take steps to prevent you from driving if you hadn't caused harm but were clearly not capable of driving safely, by an objective test (such as a breathalyzer), but he could not impose a fine or court appearance on you.