In my study software, I recently had the following sentence:

我想我们会上一样的学校.

The context (a girl speaking to another girl who had just moved into the neighborhood) made it seem like the correct translation was something like "I think we will be going to the same school." But I had thought 一样 generally referred to things that were separate objects (though very similar), not the same exact one; and that 同一 meant "the same exact one". 

For example, "these two women came to the party wearing the same dress," would use 一样, because it's two different dresses that look the same; but "These children want the same toy" would be 同一， because it's the same exact toy.

Is my understanding correct? Could I say "我想我们会上同一个学校" instead? Why or why not?