First, as quoted by Barr, Mueller used the words "conspired" and "coordinated." Unlike the colloquial term "colluded," these terms have legal significance. "Coordination" with a foreign government would be a basis for a finding of criminal liability under the election laws, and "conspiracy" would be a criminal agreement to violate those laws. This language suggests that Mueller's report viewed the conduct through the lens of a criminal investigative process -- that is, whether the evidence met the Department of Justice standards for prosecution, including the ability to prove beyond a reasonable doubt that there was intent to violate the law.
Well, duh...Mueller was specifically instructed as follows:
"The special counsel is authorized to conduct the investigation [into]:
a) any links/coordination between the Russian government and individuals associated with the campaign of President Donald Trump;"
This specifically, for a criminal prosecutor, calls for an examination not only of the crime of interference itself but of any conspiracy to commit same, which is where the "coordination" and "conspiracy" words come into play. Of course he has to view it in the lens of DOJ standards for prosecution and whether the burden could be met.
This interpretation is further supported by Barr's discussion of the obstruction allegations. Barr's language dismissing those allegations is strikingly similar to that used by Mueller with respect to the Russia investigation: Barr said that he and Deputy Attorney General Rod Rosenstein "have concluded that the evidence developed during the Special Counsel's investigation is not sufficient to establish that the President committed an obstruction-of-justice offense," echoing Mueller's statement that the investigation "did not establish" a conspiracy.
Again, this is a rather brainless recitation of the obvious from a prosecutorial standpoint, the difference on the obstruction claim being that it was a closer call that Mueller might not have felt that he had the authority to make, which is why he punted it upstairs.
Barr's letter to Congress makes clear that there was substantial evidence supporting the possibility that the president obstructed justice -- enough that Mueller did not feel he could draw a conclusion -- but that Barr nonetheless concluded that prosecution was not warranted.
It is important to keep in mind that "substantial evidence" isn't even a civil law standard (the lowest standard is a"preponderance" of evidence, but criminal charges require a "beyond a reasonable doubt", which Mueller most likely didn't have for obstruction. That does not mean that there isn't plenty of smoke in the evidence he had, but not enough for a fire.
By using the same language that Mueller used with respect to "establishing" coordination with Russia, Barr's letter suggests the possibility that, rather than "no evidence" of collusion, Mueller did find such evidence -- but similarly did not conclude it warranted a criminal prosecution.
Given Lawfare's obvious anti-Trump bent over the past two years, this seems to be more wishful thinking on the conspiracy/coordination evidence but of more import on the obstruction evidence: I obviously haven't seen the report (and neither have the Lawfare writers) but reading the tea leaves that obstruction is where the House Dems will get the most traction. However, since the standard for impeachment is also "beyond a reasonable doubt", regardless of how politically uncomfortable it gets for Trump, the fact that Special Counsel didn't find that the evidence of either conspiracy/coordination or obstruction rose to that level, the House will be hard pressed to argue otherwise.