It is just words as far as I know. Just showmanship. Brink's Place was also called the Showplace of the Nation. Since Brinks place was closed down in '52, maybe BHCC decided they would then use the title.

As for the age of the Matchbooks, the only way I can tell is looking at the Phone Number. The BHCC on the right is the older of the two. It has a 6 digit number, while the one of the left is the more modern 7 digit. Note it is during the transition when people are use to the HI letters followed by the extra number. Late 50s early 60s. The other is a has HI followed by 4 numbers 40s mid 50s matchbook. The Brown Jimmy Brinks, I have no clue on age. Could be a 30s matchbook. Pure quess work, based on the other 4 matchbooks I have from Brink's operations. Brinks bought the Lookout House in 1933 and ran it till it closed in 1952.