value
refers to the value of an input element (or textearea)
<input value="hello world">
value would be "hello world"
(or any value typed inside)
innerHTML
refers to the contents inside an HTML element.
<div>
<span class="hello">
All tags and their children are include in innerHTML.
</span>
All this is part of innerHTML.
</div>
innerHTML of the div tag would be the string:
'<span class="hello">
All tags and their children are include in innerHTML.
</span>
All this is part of innerHTML.'