Am I right that what geth calls the coinbase is the same thing that parity calls the author?
Yes, but it's called
--etherbase in Geth:
--etherbase value Public address for block mining rewards (default = first account created) (default: "0")
And for Parity it's
--etherbase will work too:
--author ADDRESS Specify the block author (aka "coinbase") address for sending block rewards from sealed blocks. NOTE: MINING WILL NOT WORK WITHOUT THIS OPTION. (default: None) --etherbase ADDRESS Equivalent to --author ADDRESS.