Is a certificated pilot considered to be a student pilot when training in a new category or class?
No.  The regulations that apply to a student pilot do not apply to the private pilot working on a new category or class rating.

§61.81   Applicability.
This subpart prescribes the requirements for the issuance of student pilot certificates, the conditions under which those certificates are necessary, and the general operating rules and limitations for the holders of those certificates.


The required endorsements for a private pilot working on a new category or class rating are also different.  Student pilots are required to have endorsements for pre-solo flight training, a solo endorsement each 90 days and an endorsement for each cross country.  The student pilot must also abide by all the limitations placed on those endorsements by the recommending instructor.
A private / commercial / ATP pilot working on a new category or class rating is required to have one endorsement.  Again, any limitations placed on the endorsement by the recommending instructor must be followed.

To act as pilot in command of an aircraft in solo operations when the pilot does not hold an appropriate category/class rating.
I certify that (First name, MI, Last name) has received the training as required by § 61.31(d)(2) to serve as a PIC in a (specific category and class of aircraft). I have determined that he/she is prepared to serve as PIC in that (make and model) aircraft. Limitations: (optional). /s/ [date] J. J. Jones 987654321CFI Exp. 12-31-19

Required endorsements for FAA certificated pilots are found in AC 61-65.