Not just SSD, but in RAM also it's faster, for the same reasons (page-based access to caches). Basically you should always use a B-tree whenever you need the functionality of an STL map.
It is faster in RAM, on SSD, on HDD, for the same reason: the reads are done in blocks. Even if you want a single byte, the system (the controller) will read an entire block, typically on the order of 100k bytes. So if your B-tree node is all stored in one block, all reads from that node will be fast.
IOW what makes it faster to access sequentially on SSD