JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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The difference between the two is that input box will allow you to add one line of text, while the Text Area will allow you to add multiple lines of the text.
Text Box (input box) is also useful if you do not want your users to leaving a lot of text in there, while Text Area can be set to resize and allow the user to nicely format their text and span them across different lines if needed.
We have also made the Text Area to be possible to be turned into a Rich Text editor, not only a plain Text Area.
I hope this explains it properly, but if you have any questions, feel free to let us know of them Louis.