Not equivalent, inclusive of. Starting to do x can absolutely include getting ready to do x.
When I'm starting to go to bed, I usually take the dogs out one last time, go turn the lights off, etc.
When I'm starting a new team, that might mean selling execs on the idea that I need headcount, finding space for them to sit, etc. all of which are also getting ready.
> For one, getting ready means you have NOT started to do the thing.
Started and starting are very very different.