Is the ECW Championship actually a world championship?

I mean it's the only championship on the ECW brand, so it's supposed to be a world title. The ones who challenge for it or hold the title are ECW's main eventers. But i'm not sure about the ECW Championship being a world title, because sometimes they act like its a world title, but sometimes they act like it's a title just like the IC or US title. It was a world title when RVD held both the ECW and WWE title. It was a world title when Bobby Lashley, Mr. McMahon and Jack Swagger were champions (remember when Jack Swagger faced John Cena, champion vs champion match). Also when Big Show was champion (remember ecw champion big show vs wwe champion john cena vs world heavyweight champion king booker). It was a world title when undertaker had to choose between the 3 top titles for wrestlemania in 2007. But lets face it, it was not a world title when chavo guerrero entered the royal rumble being champion and unlike the wwe and world heavyweight champion, the ecw champion doesn't always defend his championship on a pay-per-view. The money in the bank winner never cashes in the money in the bank on the ecw champion, that's the reason why Christian didn't win because he would most likely be the first to do that. Royal Rumble winner never chooses to win the ecw title at wrestlemania. And many people in WWE are not interested on ever winning the ECW title so to me it's not a true world title. Most of the former ECW champions went on to become a midcarder again when they move to either Raw or Smackdown. Only a few has gone on to win the World Heavyweight Championship like CM Punk.