The difference is obvious: When you apply for a permit the police consider traffic conditions and only give the permit if it will not be disruptive. That is why parades in Manhattan are held only on Sundays, and only on certain roads that drivers know to avoid on summer Sundays. And of course they are publicized well in advance. The NYPD has now reached its limit on major parades and no longer issues new permits, because there aren’t enough summer Sundays for them, and the needs of traffic come first.
There is no first amendment right to an automatic protest permit; the right exists only to get permits on the same basis that everyone else does. The police can’t discriminate between applicants based on the cause they’re promoting; rather, in each case they must consider only how disruptive it will be to traffic.