chrysalis vs. cocoon

So my daughter was doing her homework, making a vocabulary list that included the word chrysalis, which her teacher defined as belonging to either a butterfly or a moth.  I had always understood that butterflies make chrysalides and moths make cocoons, so I started to do some research.  It's tricky to get basic information, it turns out, and I looked at several websites including some other nature bloggers' pages. 
What I determined was this:  A butterfly has a chrysalis and a moth may have a cocoon.  Some other insects may also make cocoons.  The chrysalis is not made by the butterfly, per se - it is the "skin" that the creature has while the pupal stage is developing.  When the last larval instar sheds, the creature becomes a chrysalis while it pupates.  A cocoon, on the other hand, is created (not grown) by the moth larva to keep itself safe while it pupates.  It is spun with silk, and occasionally incorporates other materials into the casing.  So the chrysalis grows, and the cocoon is built.  I think - if you know otherwise, or more, please let me know!