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During the service in St George's Chapel we repeatedly saw bird-eye views of the Choir with the Garter stalls. It was visible that there were two Spanish and two Dutch royal standards for the Garter Knights Juan Carlos, Beatrix, Felipe and Willem-Alexander.
When King Felipe VI ascended the throne, he actually adopted a slightly different standard , which was considered more "historically accurate" than his father's. The most eye-catching difference, which you can clearly see looking at the banners hanging in St George's chapel, is that the Lion Rampant in the second quarter has a purple-like color in King Felipe VI's standard and a bright red color in the standard of King Juan Carlos. There are also different designs for other charges like the tower in the first quarter and the chain in the lower right quarter. The heraldic description of those charges, I believe, is actually the same, but their realizations are different.
King Willem-Alexander's and Princess Beatrix's banners in the chapel are, on the other hand, identical if I am not mistaken.
During the committal service, one could also get a glimpse of King Harald's, King Carl Gustaf's, and Queen Margrethe's banners of arms, and also of the Imperial Seal of Japan, which was used by Emperor Akihito.
Curiously, it was easier to see the banners of the Stranger Knights than those of the members of the British Royal Family themselves because of their position in the chapel and the angle of the camera.
Finally, the reason why Grand Duke Henri and King Philippe were present at the Abbey Service and not at the committal is unclear. Obviously, either they were not invited or, for some other reason they could not attend (like Queen Letizia or CP Frederik, who had other urgent engagements). Both Henri and Philippe are third cousins once removed of the late Queen Elizabeth II (in her line of descent from King Christian IX via Queen Alexandra) and both Philippe's uncle and Henri's father were Knights of the Garter. I find it unlikely that they would not have been invited to the committal unless there was a Knights/Ladies of the Garter only rule, but, as you said, that was not the case based on the presence of the Greeks and the Romanians.