Inspired by the confusion in the comments on [this question](https://math.stackexchange.com/questions/15188/how-to-prove-a-subset-b-b-subset-c-c-subset-a-rightarrow-b-c):

I always thought that the standard was to read $\subset$ as "is a strict subset of", and $\subseteq$ could mean proper or improper inclusion.

Was I wrong?