What's the difference between <a_element /> and <a_element xsi:nil="true" />?

do you know if there's a difference between these tags on XML/XSD?

<a_element /> and <a_element xsi:nil="true"/>

e.g:

<SpreadCurve>
      <Index>3M</Index>
      <IndexNumber>4587</IndexNumber>
      <BusinessArea xsi:nil="true" />
</SpreadCurve>

and

<SpreadCurve>
      <Index>3M</Index>
      <IndexNumber>4587</IndexNumber>
      <BusinessArea />
</SpreadCurve>

Are these equivalent ?

If I have a XSD element:

<xsd:element name="BusinessArea" type="xsd:string"/>

this means that it is by default xsi:nil="false". And this means it will not accept a null value for this element.

My doubt is, will it accept this one?

<BusinessArea />

What does this really mean to the XSD?

Best regards