One filibuster was over ensuring that you are allowed your constitutional liberties, and the other was over making sure the government can limit your constitutional liberties.
This first filibuster was initiated by Senator Rand Paul over the issue of whether or not the government has the ability to commit drone strikes on U.S. citizens without first giving them due process.
This second filibuster was started by Senator Chris Murphy in an attempt to further push the Democrats gun control agenda after the recent horrific terrorist attacks in Orlando. Murphy, unlike Paul, wants to ensure that the government can just add you to some arbitrary list without any due process.
Also, Rand was the only one involved in the first filibuster, whereas in this filibuster tons of Democrats decided to use it to campaign against guns.
Sounds like a pretty big difference to us.