I am treating "wavefunction collapse" as a generic term for "whatever it is that causes 'me' to see the outcomes that I do." Orthodox views treat this wavefunction collapse as an extra "measurement" rule and then mumble around the issue of what exactly constitutes a measurement, usually trying to say that none of it is 'physically real' so such questions are moot. Many Worlds treats the wavefunction collapse as a parochial artifact of having been in a particular Everett branch and figuring that out by becoming entangled with some particular other particles.

But I agree that if one defines wavefunction collapse to be only that sort of instantaneous updating to only one particular state that the orthodox views take, then Many Worlds language just does away with it all together. I prefer to use the same term for both phenomena because I have found that it helps people who are uneasy with MW to realize that it's not all that weird.

In my view, the result of the linked paper weakens the orthodox position of denying that "wavefunction collapse" is physically real.