Someone here will be able to tell you the approximate age of the button based on the DVC logo at the bottom - at different times there were two mountains vs. three. I can't remember which came first, but there are people here who do!
Pin Trading became a big thing at WDW & DL around the time of the Millennium Celebration 1999-2000. Pins were available prior to that and for the most part they are something you buy. Pin trading was always a big thing at Olympic events around the world and I believe still is. Buttons are more commonly used as give away items although there are some available to buy. Conversely there have been times that pins were given away to commemorate certain events. The two round items in your pictures are Buttons although they aren't always round. Buttons are typically a tin type of material covered with a printed image and then a plastic coating over the image, sometimes the pictures are just printed directly on top of the tin. The center image is what is classified as a pin and normaly is a hunk of metal that is filled in with colored enamel which these days is now really a type of resin. Both have been available for years and still are today. I don't remember what year they actually did away with the mountains in the DVC logo but the information I can find says it was changed in 2011 to the blue Mickey Head globe logo. Also says the three mountain logo was changed in 1996 to the two mountain logo that is on your buttons. I joined in 1996 and only remember the two mountains which I always preferred to the Mickey Head globe. So your Pin was made for 2000 but the buttons could be from whatever year the resort opened through 2011. Someone more familiar with HHI may be able to tell you which of the two is older.