No I don't think so, I think these are both made by the same firm; t'other Anne said above, "Libochovice Glassworks, patt.no.1691." which is true as they are shown in the 1950s Libochovice catalogue as such, but the Reg Design no dates from 1934 registered by Heppner Ltd (who were agents not manufacturers, as Bernard also says above.)
In 1934 the company wasn't Libochovice (which was a post-war Sklo Union factory name - i.e. part of the state owned glass conglomeration marketed under the Sklo Union name). It was then Feigl & Morawitz (info courtesy of Sklo Union Art Before Industry: 20th Century Czech Pressed Glass, by Marcus Newhall) and so far we have seen only one earlier (from the 1920s) catalogue for them.
As to numbers not being on every piece of a pattern, David C Watts, author of Glassmaking in London, explained to me last year that in his experience only around 1 in 4 moulds carried the RD no information. Bernard has also told us elsewhere on the board that some wholesale or retail customers didn't want anything on the pieces they bought to indicate who had made it, and the glassworks were always willing to oblige in the interest of a sale.
Variations could well have been made in glass and possibly crystal for different customers and not all those variants are shown in catalogues. Regular lines would be of course, but if something was made just for one buyer then it may not show up anywhere else.
F&M / Libochovice are known to have made a wide range of glass from fairly basic utility glass to high quality well-finished glassware so anything's possible. My opinion (for what it's worth!) is that both your items are genuine but I can't prove it as yet.