To answer the question in your title:
If two* APs are publishing two different SSIDs but still bridging client traffic onto the same VLAN in the standard, straightforward manner, then clients of those SSIDs will be able to see each other.
[*two: A single box that can publish multiple SSIDs, or the same SSID but on different channels/bands, is technically acting as multiple APs per the language of the IEEE 802.11 standard, even if it's all in one box.]
If that's not working with your particular brand/model of equipment, then that's a matter of figuring out what kind of proprietary filtering or other traffic-manipulation your vendor is doing to your traffic. Your question becomes: What exactly is my Buffalo AirStation Pro doing to my traffic when I have "Wireless Client Isolation: SSID Isolation" enabled, but with both SSIDs bridged to the same VLAN? But that's a different question than what you put in your title.