They are both used to receive Bitcoin over the Lightning network.
However, a Lightning invoice is good for one single use. It typically requires the recipient to set an amount, although some wallet clients do support an unspecified amount. A Lightning invoice also expires after a length of time, with some wallet clients not making it apparent what that time is or how to set it, if possible.
A Lightning address does not have these characteristics. Anyone can send to one at any time, as opposed to asking the recipient for an invoice beforehand every time.