It is the same log in information. Just enter your user name and posting key and you are good to go.
Yes they both use the same blockchain (data) so they will reflect everything done on the other. Busy is a bit slower registering some things done on steemit and vice versa but they catch up (I presume once everything is verified on the blockchain).
I am more comfortable on steemit since I am here two months but I am doing more on busy.
In other words "Six of one, half-dozen of the other." Ha, I understand. I wish I would have known about Busy the last few days when Steemit was acting like a spoiled child on the cookie isle. Thanks.