I'm not the ultimate expert, Greg, but I think they are about the same thing. Themes and templates are both html, but most WordPress users don't mess with code. Maybe 'theme' is just a less scary word?

Leslie

WordPress themes are much more than a template made with html and css. They include php and sometimes js.
A design is not a template but both themes and templates are based on designs.
I'm sure I complicated the concepts for you even further.

Here you can examine the anatomy of a WordPress theme. You can see that design is just a small part of it.

Theme is about Look and Feel of website with plugins and options.
Template is about layout of a page e.g. Full width template, Right sidebar template, Left sidebar template.
A theme can have many templates.

Different language is used depending on the platform chosen to develop.

Wordpress, Joomla and Drupal don't share the same naming conventions, so it's all dependent of the system being used.

Joomla uses Templates and Drupal uses Themes to describe essentially the same thing.

In development plugins, extensions and modules should not be correlated with theming or templates, but rather elements that extend these things. I think Wordpress is limited in this respect, because the two tend to be so intertwined so much , but like I said before it's how the group or company using those system to define the language. Not always set in stone