Clear and delete are two different actions.
Most messaging apps offer both Clear Chat, which removes every message but leaves the conversation itself in your chat list, ready to be used again, and Delete Chat, which removes the conversation entirely from the list. It is easy to tap the wrong one and assume the job is done, when in fact an empty but still present thread is not the same as a thread that no longer exists on your phone at all.
Neither action reaches the other person's phone. Clearing or deleting a conversation on your device removes it from your device, and the same conversation continues to exist on theirs unless they take the same step separately. Worth remembering before assuming a conversation is gone simply because your own screen no longer shows it.
On WhatsApp specifically.
Open the chat, tap the contact name, and Clear Chat sits under a menu usually labelled More or found via the three dot options at the top of the conversation list. A newer option, Delete Messages For Everyone, works only within a short window after sending and only removes the specific messages you select, not the whole history, so it is not a substitute for clearing an entire thread. Reach for it when a single line went out by mistake, and reach for Clear Chat when the whole conversation has run its course.
Media saved from a chat to your phone's own photo gallery survives clearing the chat itself, since the two live in separate places once the media has been downloaded and viewed, a distinction worth keeping in mind before assuming clearing a chat removes absolutely everything connected to it.
On Telegram specifically.
Telegram's Clear History option, found in the same contact menu, offers a further choice, clearing the history for yourself only or for both participants, the latter working even outside any time limit for a normal chat, unlike WhatsApp's short window. This makes Telegram somewhat more thorough for anyone who wants a conversation gone from both phones rather than only their own, without needing the other person's cooperation to make it happen.
A secret chat, covered in our guide to Telegram secret chats, goes further still, since deleting it removes the conversation from both devices immediately by design, without a separate for everyone option ever being necessary in the first place.
The backup that quietly undoes all of it.
Both WhatsApp and Telegram can back chats up to iCloud or Google Drive, and a backup taken before you cleared a conversation still contains it in full. Restoring the app from that backup, on the same phone or a new one, brings the cleared conversation straight back, which surprises people who assumed clearing was permanent.
Check your backup settings under the app's own Chats or Settings menu, and either turn backups off for the app entirely or delete the specific backup after clearing a chat you actually want gone for good. On an iPhone this usually means checking Settings, your Apple ID, iCloud, Manage Storage, and on Android the equivalent sits under the app's own backup preferences tied to your Google account.
Linked devices and web sessions.
WhatsApp Web and the desktop app mirror your phone's chats live, so a chat cleared on the phone clears there too, but a browser tab left open on a shared computer can still show the conversation until the page refreshes or the session is closed. Check Settings, Linked Devices periodically and log out of any session you do not recognise or no longer use, a habit worth forming even for guests who never book on anything but their own phone.
Desktop apps on a shared computer.
A work laptop or a family desktop running WhatsApp Web or the Telegram Desktop app is worth its own moment of thought, since the browser or app itself can cache recent messages locally even after a chat is cleared on the phone that owns the account. Logging out fully, rather than simply closing the window, is the more reliable habit on any computer you do not fully control.
Browser history and autofill are a smaller version of the same risk, since a search bar that remembers a recently visited web.whatsapp.com session can be enough to prompt a question you would rather not answer on someone else's screen.
A short routine worth adopting.
Clear the thread once an evening is confirmed and done, check that no backup will quietly restore it, and glance at linked devices every so often. It takes less time than the booking message itself, applies exactly the same whether the arrangement was a travel companion trip through Schiphol or an evening in the city, and companions filed under athletic or brunette are confirmed through the same thread either way, with the rates page carrying the only figures worth keeping a note of at all.