SRAM is a privately-owned corporation based in Chicago in the United States. Its manufacturing operations are based in Portugal, Taiwan, and mainland China. Unlike Campagnolo and to a lesser extent Shimano, SRAM has extensively acquired other cycling-related companies like Zipp, Quarq, and TIME Sport pedals.
By my recollection, when SRAM got into the road groupset market in the mid 2000s, they initially led with Force as their tier 1 group and Rival as their tier 2 group. They launched Red as their tier 1 group in 2007 (and demoting Force and Rival by one tier each). Bicycling Magazine attests that Red was named after SRAM's corporate color. My recollection is that 10s and 11s Red were very light groups. SRAM differentiated Red from Force with red accents (obviously), and initially they made Red cassettes out of a single machined block of steel. By contrast, SRAM's, Shimano's, and Campagnolo's other cassettes are made of loose cogs, many of them pinned to spiders in groups of 2-3. Also, SRAM appears to have historically branded RED in all caps, and Force and Rival in normal case. For example, this quote from SRAM's own corporate history page (accessed November 2021):
By 2004, SRAM planned a return to the road and began the development of two new road groupsets. SRAM brought Force and Rival to market in 2006 and Force was raced in the Tour de France the following year ... In 2008, SRAM introduced a new premium road groupset, SRAM RED.
(NB: Many cycling media outlets write Red in normal case, which I have elected to follow.)
It may also be worth mentioning the history of Quarq, which was a standalone company that manufactured spider-based power meters. It was acquired by SRAM in 2011. SRAM maintains Quarq as a standalone brand, including Quarq-branded carbon crankarms. These have been options for Shimano or Campagnolo users. The arms are probably comparable in quality to Force. However, SRAM also incorporated Quarq's technology into the power meters in its Red and Force AXS cranksets (which have optional power meters).
I'm currently unable to document if there's any deeper history behind the Force and Rival lines.
Google's dictionary gives two definitions of heritage that are possibly relevant to this discussion:
valued objects and qualities such as cultural traditions, unspoiled countryside, and historic buildings that have been passed down from previous generations
denoting a traditional brand or product regarded as emblematic of fine craftsmanship
Focusing on the question title rather than just the history of each individual groupset's name and branding, SRAM's overall heritage as a company is potentially relevant, since it affects how each groupset is perceived by the public. SRAM is a recent entrant into road cycling. In that sport, it currently has much less heritage in the traditional, historical sense than Campagnolo, with Shimano being intermediate between Campagnolo and SRAM.
I'd argue that SRAM is trying to build heritage through innovation instead. They were the first to a quality, operational wireless shifting groupset. They were early pioneers of hydraulic disc brakes on road bikes. SRAM's integrated power solution is generally considered to be accurate (e.g. this review of the 2017 Quarq DZero), whereas Shimano was later to develop their own integrated power meter than SRAM, and their last generation of units had accuracy problems, and Campagnolo don't have an integrated unit of their own. SRAM's wheel design, which they achieve through owning Zipp, has generally been considered good, and it has been clearly ahead of Shimano's.
Innovation does ebb and flow. Both Campagnolo and Shimano have been clear innovators in the past, and even in more modern times Campagnolo tends to release drivetrains with more gears first and Shimano was the first to a high-quality commercial electronic drivetrain. Zipp appears to be pulling ahead through innovations in power and electronics. All three companies are horizontally integrated to some extent, but I'd assume that SRAM will continue to leverage Zipp's experience and technology to build perceptions of quality and innovation on the wheel side as well.