My grandfather came to the U.S. from Scotland and settled in Utica NY. He worked as a driver for a company president and carried these pistols when driving his boss between Utica and New York City.
I've got one of his NY state pistol permits from the 1930's. Too bad it's so tough to get a CCW permit in NY now!
The Colt in .32 ACP is a Model 1903 Pocket Pistol. In 1908, Colt made the same pistol in .380 ACP and called it the 1908 Pocket Pistol. (Why change a winning formula?)
The Remington is a Model 51. It was also made in .32 ACP, but not so many.
Both pistols are excellent designs and were machined from bar stock by hand. They are not considered 'powerful' cartridges these days, but unless badly fouled or internally broken, they are very functional and reliable pistols. Your Scots Grandfather had good taste.
That Colt has been handled and carried a bit; it looks like most of the blue is worn off. Pity, but it gives it a personal feel.