End-to-end-encrypted means without significant, unexpected breakthroughs in mathematics, no one can read it between the sender and the recipient, even if the traffic pass through FSB, NSA, Telegram, Google and Facebook headquarters and they all conspire to break it.

Point-to-point-encrypted means it can theoretically[1] be read by the vendor (Telegram in this case) or anyone who can coerce the vendor. This is the standard for mail, online banking etc.

The reason for providing both end-to-end-encrypted and point-to-point-encrypted is that point-to-point-encryption is significantly simpler, which makes it easiee to create useful and or cool features.

[1]: vendors can do a nunber of things to make it hard/next to impossible for employees and others to access data, like for example restricting access to user data to service accounts, only allow debugging access in special circumstances and auditing such debugging access.

Telegram used to claim they solve it by sending/storing encrypted data through/in different data centers from the keys, and keeping these days centers in different jurisdictions. Done properly should mean that two or more employees across the company would have to conspire to get access to customer data, or two or more judges in different countries would have to demand data.

But unlike with end-to-end-encryption we have to take their word for it.

Building over eitland's reply, Telegram allows users to see messages on several devices. This is because they terminate encryption on their servers and can send a copy of the plaintext message (re-encrypted) to every other device of the same user. They also store a copy because you can start from scratch with no surviving devices and a brand new one. All you need is access to your account. E2E chats work only on one device and are invisible to the other devices of the user [1]. More technical details at [2]

[1] https://telegram.org/faq#secret-chats

[2] https://core.telegram.org/api/end-to-end