Which method allows users to send short messages from one mobile phone to another?

Text messaging is a method specifically designed for sending short messages from one mobile phone to another using mobile networks. This communication method has been widely adopted due to its simplicity and effectiveness. It enables users to exchange brief messages without the need for an internet connection, as it utilizes the cellular network for transmission.

In contrast, email is primarily structured for longer form communications and typically requires an internet connection, making it less immediate and less suited for quick exchanges compared to text messaging. Instant messaging, while also facilitating real-time communication, usually relies on internet connectivity and is often used for more interactive conversations, including multimedia sharing. Social networking involves sharing content and updates on platforms, which is not a focused method for sending brief messages directly between mobile phones. Therefore, the context and functionality of text messaging distinguish it as the correct answer for this question.