Look at from the perspective of the computer. It steps through the list of assets, one-by-one. For each asset, it then steps through the software titles one-by-one. Your WHERE conditions are evaluated at each individual pairing of asset + software. As presented, your condition is saying
For this asset, for this specific piece of software, is the software both MozyPro AND Spotify?
If I'm reading your requirement correctly, what you want to be saying is
For this asset, for this specific piece of software, is the software either MozyPro OR Spotify?
For each asset, as the process steps through each associated piece of software, it will then process it...
Software: Microsoft Word; is the software either MozyPro (NO) or Spotify (NO); no yeses means exclude
Software: MozyPro; is the software either MozyPro (YES) or Spotify (NO); we've got a YES, so include in the output
Software: Adobe Reader; is the software either MozyPro (NO) or Spotify (NO); no yeses means exclude
Software: Spotify; is the software either MozyPro (NO) or Spotify (YES); we've got a YES, so include in the output
etc.
Change your WHERE condition from an AND to an OR and see if it produces what you're looking for:
Where
tblSoftwareUni.softwareName Like '%MozyPro%'
OR tblSoftwareUni.softwareName Like '%Spotify%'