What is the difference between hiking boots and backpacking boots?

If like you say there's going to be a "couple of overnight journeys" then it would be wise to go for the backpacking boots. When we're hiking Sedona on fairly easy trails, we use our hiking boots. But like the two other contributors who answered your question say, I'll have to agree that you'll have to get a pair of both especially if you also do regular day hikes on fair to moderately difficult trails.

It's about the right gear for the conditions, one pair of shoes/boots aren't going to be appropriate for both hiking in the snow and summer hiking. For three season backpacking I don't wear boots at all anymore, prefer a very lightweight running shoe. Just got back from a very wet four night trip along the north border of Yosemite Park, elevations between 5,000 and 8,000 feet. There is a lot of patchy snow still above 6,500 feet and everything is wet. Was really happy to be wearing the running shoes, when I waded across a small stream they would drain and start to dry quickly. If I was wearing boots the wetter they get, the heavier they get. The less your shoe weighs the easier it is to keep putting it in front of the other one. During the winter or snowy conditions it's a different story, you need an heavier insulated boot. I prefer Sorel for my winter boots. Last season did a 40 mile and a 35 mile hike through the Emigrant Wilderness wearing a pair of $30 running shoes. Thought the running shoes to be a big improvement over even the low topped hiking shoes/boots.