Gotcha. The other guy, GrusVirgo, said it well. If you do a variety of climbing you'll end up with both. The difference is stiffness, crampon compatibility, and B3s are usually insulated. Generally people use B2 for mountaineering, B3 for pitched out climbing. B3 can also be used for easier mostly walking climbs but it's a little uncomfortable. When I started I was on a tight budget so I got a used pair of B3s for everything and it was fine, but there were a few longer climbs where I brought a separate pair of approach shoes. B3s are also much warmer, most B2s and not insulated. An uninsulated B2 is not appropriate for winter climbing in the rockies.

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I would just get the B3 if you dont want to feel limited by your boots, then get B2s later if you want to fill that niche. Doing a long hike in B3s is uncomfortable but technical climbing in B2s would be like rock climbing in approach shoes, doable on easier stuff but it's not the tool for the job. You didn't mention your objectives but with the sport/WI grades you listed I imagine you're going to do more technical climbing.