For the duration of my response, I shall refer to text input as a 1 line form input and textarea as a multi-line form input.
The textarea or text input themselves do not intrinsically determine if the message can be submitted with the enter key or not. Rather, it is the elements around the textarea or text input that signify its sending mechanism.
Here are a two examples that contradict your text input == enter and textarea == not enter theory:
Meebo instant messaging
Meebo uses a textarea, but has no send button. The only way to send a message is to hit enter. Since Meebo's design emulates a desktop instant messaging program, people expect the sending mechanism to follow the convention - hitting enter. IM applications require fast communication. Hitting enter is much faster than pointing at a submit button and clicking it.
Facebook private message
Facebook uses a 1-line text input, but doesn't require hitting enter to send the message. You can hit the reply button to send the message. The enter key sending mechanism can be turned on or off by using the checkbox next to the enter key icon. Some people may choose to turn off the enter-send because either the want the enter key to insert a line break or they don't want to accidentally send out an unrevised message. As these are personal messages to close friends, you don't want an inadvertent enter key to send out an unfinished message that could change the relationship.
The number of lines of the form input only suggest the average length you think your users should be typing. The number of lines do not convey its sending mechanism. You must design the elements around the form input to signify its sending mechanism. To actually decide on which sending mechanism to use, you need to judge how important the following factors are to your application:
- Speed of communication: Applications that require very fast communcation, such as instant messaging, should use enter-send. Apps where people generally only send messages once every hour or so will not benefit greatly from enter-send.
- Importance of the message: Is the message just some random shout-out to strangers? If enter-send were enabled, and the user accidentally hit enter, expecting a line break, but instead the message is sent out, it won't be a big deal. They'll learn from this mistake and send out another message correcting their previous one. If however, the message carries a lot of weight, using a send button would be better. You'd want the user to consciously review her words and then hit the send button. Examples include, private messages to friends, emails, and StackExchange answers.
- Form: It's a convention that forms are submitted when you hit the enter key on any non-textarea form element. This gives power users a way to quickly send the form. If your commenting system is a full blown out form requiring name, email, and message, for example, allow hitting enter on the non-textarea fields to submit the whole form. This feature is actually built into HTML. Just set the
action attribute on your
<form> tag and it's all handled automatically for you. Of course, you should also include a send button on any form for novice users who don't know this enter shortcut.