After doing some digging and talking to a few folks, it seems like the most concise answer is, "Yes," you must file a Form-D if you sell any
type of securities, including convertible-notes and equity. The best source of information, surprisingly, comes straight from the SEC website - www.sec.gov/answers/regd.htm . The size of a raise determines how significant the disclosures, financials, etc. that must be given to each potential-investor so they can make a "smart" decision as to investor or not invest. They reference the laws ("Rules") that dictate the requirements at different thresholds: Rule 504 (up to $1mm), Rule 505 (up to $5mm), Rule 506 (> $5mm). It seems like "accredited investor" is a critical term, too, and if you only sell to accredited investors, you can advertise your offering publicly. Pretty interesting stuff, actually.
I'll keep digging into the individual state laws / filings, but at least this is a start. Please feel free to chime-in if you have experience with this!
[I should disclose that I am an engineer and NOT an attorney - consult a securities attorney before using any advice I share on this thread]