Both types of rooms are designed for two people, but in a twin room they sleep separately, and in a double room - together. See what are the other types of hotel rooms and abbreviations.
In many cases, hotels do allow two people to stay in a room booked for one. However, it is crucial to communicate this requirement at the time of booking to ensure appropriate room assignment. Some hotels may charge an additional fee for the second guest, while others may include it in the standard room rate.