Take these two original paths, sent by router with ASN 111 to an eBGP peer:

10.0.0.0/16 169.254.1.2 0 100 111 65111 65222 7224
10.1.0.0/16 169.254.1.2 0 100 111 65111 65222 222 7224

Applying remove-private-as has no effect on the second, since the path contains public ASNs.  The paths receiveced by the eBGP peer will look like this:

10.0.0.0/16 169.254.1.2 0 100 7224
10.1.0.0/16 169.254.1.2 0 100 111 65111 65222 222 7224

But doing remove-private-as all will literally remove all private ASNs:

10.0.0.0/16 169.254.1.2 0 100 7224
10.1.0.0/16 169.254.1.2 0 100 111 222 7224

However with remove-private-as all replace-as the path will have the same length, but with each private substituted with public of the advertising peer:

10.0.0.0/16 169.254.1.2 0 100 111 111 7224
10.1.0.0/16 169.254.1.2 0 100 111 111 111 222 7224