no the value attribute refers to a JSF value expression. Thus you can do value="Hello World" or value="#{managedBean.propertyName}".
A component id is just a static id used in HTML that you use in dom.
I am assuming that you want to output text somewhere in the page that has been typed into an input text field. To do what you want you need a more rich environment than just JSF components. You can add something like ajax4jsf or use a component suite like Trinidad. THere are others as well.
Both would provide you seamless updates triggered by text completion in input text field and move the text to the output text field without having to push a button causing a page submit.