Ah, yes, the top one is not the same as the second one – compare the HTML:
<form id="searchform" action="https://www.priestcomputers.nl/" method="get" role="search">
<div>
<label class="screen-reader-text" for="s">Zoeken naar:</label>
<input id="s" type="text" name="s" value="">
<input id="searchsubmit" type="submit" value="Zoeken">
</div>
</form>
The first one seems to be a widget? You added?
Is the second one part of your theme? What theme?
<div id="headerSearchDiv" style="padding-right:0px;">
<form action="https://www.priestcomputers.nl" method="get" role="search">
<input id="headerSearchField" style="opacity: 0; " onclick="this.value = '';" value="" title="Search Site" name="s">
<input id="headerSearchSubmit" type="submit" value="">
</form>