In the UK we have far too many hangups about whether it is a bus or a tram or a train. The countries that do public transport best treat it as an integrated network and it's not too important what mode operates each link. They do however often have a distinction between "normal transit" (buses and street running trams serving all stops without significant priority measures) and "rapid transit" (highly segregated and limited stop, whether priority bus, light rail or heavy rail). So I would paint express buses serving non-Metrolink corridors in the Metrolink livery, and other buses in the same livery but with orange instead of yellow to hark back to the last time Manchester had something resembling an integrated transport network. Trains are more difficult because most routes operate outside Greater Manchester and even those that stay within tend to share diagrams with those that go outside, so perhaps a different livery is more appropriate here.
I think we are running before we can walk here (a not entirely inappropriate phrase).
Firstly, it has not yet been decided whether Bus Franchising will be adopted.
Secondly, whatever Reforms are adopted, the first priority is to arrest the accelerating decline in bus usage. I understand that detailed analysis by the various parties has revealed that patronage is lower than was initially believed.
Thirdly, the "environment" is not right for Integration, apart from possibly some progress on fares. Punctuality of ALL modes is nowhere near good enough and Reliability of (at least) Metrolink, Northern Rail and one or more bus companies is also poor. There are far too many obstacles in the way for buses to be punctuality, from bus stop blocking, through poor road layout, frequent road closures due to unannounced roadworks, accidents and "police incidents"*, poor information on said closures (If you aren't on Twitter, you don't exist!); and most of all, traffic light co-ordination.
Fourthly, the waiting/connection environment is poor, with long walks between modes (or even bus to bus), and no protection from the elements (both climatological and criminal).
A chain is only as strong as its weakest link!
As regards liveries, I'm not sure what taxis have got to do with anything, but all I know is that IF franchising is adopted, every colour/combo except predominantly red or (light) blue are still options.
*People with more knowledge about such things than me, tell me that nowadays, the Police treat every reported Road accident as a potential crime, and so lane/road closures last far longer than they used to.