The button with an anchor surrounded by a wreath and a rope border is very similar to a British Royal Navy button, but it is a "backmarked" hollow 2-piece button, which didn't exist until about two decades after the 1812 addition of a crown above the anchor on the Royal Navy buttons. I suspect your button MIGHT be a British Merchant Navy Officer's button. Its hollow 2-piece brass construction and a back saying "Quality" in indented letters indicates it was manufactured sometime in the mid-to-late 1800s.
The four-hole "advertizement" button with raised lettering and "serifed" letters also tends to date mostly from the mid-to-late 1800s. That type of button was used on long underwear ("longjohns") and for pants-fly closure, not for shirts and coats.