Collectables can be turned in at any Collectable Appraiser. The Scrip Exchange, who sits next to the Collectable Appraiser, will accept your scrips and offer gatherer and crafter gear, Soul of the Crafter, Master Recipe Tomes, Tomes of Regional Folklore, gatherer and crafter Materia, and other tokens and crafting materials. Each expansion's appraiser and exchange has to be unlocked separately, and doing so adds that expansion's items to all exchanges.
In a related way, the currency introduced in Patch 5.11 and earned from the Ishgardian Restoration is called Skybuilders' Scrip and is likewise earned by crafting collectables. However, the ingredients and recipes are unique to the restoration, and most materials are exclusively found in the latest iteration of the Diadem.
History of Scrips
Introduced in Patch 4.0 with the release of Stormblood, Yellow Scrips were used to purchase endgame items at level 70. Weekly limits on all scrips were lifted at the same time. Yellow Scrips were retired with the release of Endwalker and are currently exchangeable 1:1 for White Scrips.
Introduced in Patch 3.05, Red Scrips were used to purchase endgame items at level 60 and originally weekly locked to 450 just like the most recent Allagan Tomestones. They were retired with the release of Shadowbringers and were exchangeable for Yellow Scrips until Endwalker launched.
Introduced in Patch 3.0 with the release of Heavensward, Blue Scrips were used to purchase items at levels 56-59. They were retired with the release of Stormblood and were exchangeable for Red Scrips until Shadowbringers launched.