Quick answer
On Android, stickers you receive are saved as WebP files in Internal storage › Android › media › com.whatsapp › WhatsApp › Media › WhatsApp Stickers (on older Android versions, Internal storage › WhatsApp › Media › WhatsApp Stickers). Packs you install are held privately by WhatsApp and the sticker app, not in that folder. An iPhone has no visible sticker folder at all.
Android: the WhatsApp Stickers folder
Every sticker that arrives in a chat is saved to your phone as a small WebP image. On current Android versions WhatsApp keeps its media under the Android › media folder, so the stickers you have received sit in a folder of their own called WhatsApp Stickers, next to WhatsApp Images, WhatsApp Video and the rest.
- Open your phone's Files app (Files by Google or the maker's own file manager).
- Go to Internal storage, then Android, then media.
- Open com.whatsapp, then WhatsApp, then Media.
- Open WhatsApp Stickers. Each sticker is a .webp file.
On phones that have not moved to the newer layout, the same folder lives at Internal storage › WhatsApp › Media › WhatsApp Stickers. The files are named by WhatsApp rather than by pack, so a long chat history can leave hundreds of them, and clearing them frees space without touching your chats' text.
Installed packs are not a folder of files
A pack you add from Sticko or another sticker app does not appear in the WhatsApp Stickers folder. When you confirm Add to WhatsApp, WhatsApp copies the pack into its own private app storage, which file managers and other apps cannot open, and the sticker app keeps its own copy.
That is why deleting files from the WhatsApp Stickers folder never removes a pack from your tray, and why a pack has to be added again from the sticker app after WhatsApp is reinstalled or moved to a new phone.
iPhone: no sticker folder to browse
iOS keeps each app's data inside the app, so there is no WhatsApp folder in the Files app and no way to browse sticker files directly. Stickers you receive stay inside WhatsApp, and packs you add stay in your sticker tray.
To keep a sticker you like, tap it in the chat and add it to your favourites; it then has a permanent place in the tray. When chat backup to iCloud is on, the stickers in your chats are backed up with the conversations themselves.
Backing up and moving your stickers
WhatsApp's chat backup — Google Drive on Android, iCloud on iPhone — carries the stickers that are part of your conversations, because they are messages. Third-party packs in your tray are a different matter: they come from the sticker app, so after restoring a backup on a new phone you add them again from that app. The guide on stickers missing after changing phone walks through it.
Related: stickers missing after changing phone, deleting sticker packs, sticker size and format.
Get the Sticko app
WhatsApp only accepts sticker packs from an installed app, so the last step always happens outside the browser. Sticko is free on Android and iPhone, and adds any pack to WhatsApp in a couple of taps.