Whether you're moving from Queens to Jersey City or from Brooklyn to Philadelphia, crossing a state line makes it an interstate move. For you, the biggest differences are the route, the timing, and who's responsible for your belongings along the way.
Route first. Bridges and tunnels come with tolls, and some routes restrict commercial trucks. Ask your mover how the route is planned and whether tolls are included in your quote. With a flat-fee move, they should be.
Timing second. Longer drives mean the truck is on the road for part of the day, so plan your elevator reservations and move windows at both buildings with the drive in mind. Early starts help, especially for moves heading toward Connecticut or Philadelphia.
Finally, ask whether your belongings will be transferred to another truck or warehouse along the way. Some companies hand interstate moves off to a separate carrier. We don't: the crew that loads your home is the crew that unloads it, and that keeps both the schedule and the responsibility in one place.