There was another Hudson's Budget Store on John R near 12 Mile in Madison Heights. I understand the Pontiac Mall/Summit location was originally opened as a stand-alone HBS, and was remodeled and became a full line store later, although I don't personally recall this.

Hudson's Rainbow was a mid to late-70s attempt to re-brand & market HBS with a two-pronged approach. First was to remove the name "budget" from the name [[budget=compromise in quality in consumer's minds). Secondly, to experiment with spinning it off into a separate lower/mid-tier store. This was not to be, as the writing was on the wall.

The Dayton's half of the Dayton-Hudson parent corporation had opened its first Target store in suburban Minneapolis and the brand was successful from the get-go. That, coupled with the subsequent purchase of mid-tier Mervyn's by Dayton-Hudson completed the spectrum of a discount/mid-tier/upper end portfolio of brands. There was no longer a niche or need for Rainbow. Interestingly, Target, Wal-Mart, and K-Mart all opened their first stores during the year 1962---and the rest, as they say, is retail history.