ca_flyer made a mistake on the flying in clouds' bit, which I'm only pointing that out so nobody gets misled.
Yes, if it's a 2 hour checkout the instructor will log PIC 2.0, Dual Given 2.0. The instructor is 'legal' PIC as he is in charge.
The 'student' will log all time he is sole manipulator, which in practice means PIC 2.0, Dual received 2.0.
If it was the student's plane and he wanted to be legal 91.3 PIC (as, I think, is his right) he would log the same, as would the instructor. The student would be in charge so 'legal' PIC, but the instructor gets to log PIC because 61.51 (3) says he can. If the instructor doesn't like that arrangement then he doesn't have to go.
Very sensible, and if you want to know the story just add up the columns and subtract the dual received from PIC and you can sort of work out how many hours were solo PIC (which would be pretty close to P1 in the UK).