There is a big difference between the two.
For starters, the version of DVD Architect bundled with Vegas Movie Studio 9 supports only standard-definition authoring (and DVD Architect Studio 4.5 has not been updated since the Vegas Movie Studio 9 series was first released) while DVD Architect Pro 5 (as bundled with later releases of Vegas Pro 8 and all versions of Vegas Pro 9) supports high-definition authoring in addition to standard-definition authoring. In addition, the Pro supports rendering to many more audio and video formats than the Movie Studio does. Plus, if your videos are of the 1280 x 720p60 format, some consumer editing packages will drop every other frame since they are capped at 30 fps maximum (I don't know whether or not Movie Studio supports anything over 30 fps, but Vegas Pro can support up to 59.94 fps @ 720p using custom settings). Finally, like the least-expensive version of Pinnacle Studio 12 (which is the basic version), the plain Vegas Movie Studio 9 is limited to standard-definition video support only; neither of those two basic versions (which retail for $50) supports high-definition videos at all. You'd need to purchase the step-up versions of those two programs - Pinnacle Studio 12 Plus or Sony Vegas Movie Studio Platinum, either of which retails for $100 - in order to edit HD videos at all if you insist on using either of those two lines of software.
I used Pinnacle Studio 12.1 Ultimate for a while, but a few limitations (such as the lack of native support for 720p60 videos or any 1080p videos) caused me to spend the extra for Vegas Pro 9 (which, by the way, is available from the Sony Creative Software Web site for $599 for the downloaded version plus $15 for the optional DVD setup disc, or $679 for the boxed "retail" package which includes the DVD setup disc). I decided to forego the extra disc and got only the download (which I could archive onto an optical disc).