One of the goals of the Islamic legal theorists is to determine what is or is not an authority in Islamic law. They are not concerned with the details of the actual law but they are concerned with the sources and methodology of that law. When they define the word Sunnah, they are defining it from that perspective. Therefore, when it comes to the reports that have been narrated about or from the Prophet صلى الله عليه وسلم, they try to distinguish what is an authority and what is an example for the Muslims to follow from that which does not fall into that category. Their definition will definitely differ from that of the scholars of hadeeth, being much less broad in scope.
Perhaps the most common definition given for the Sunnah from Islamic legal theory perspective is: Whatever comes from the Prophet صلى الله عليه وسلم, other than the Qur'aan itself, in the form of his speech, actions or tacit approvals. His speech includes what he commanded, recommended, permitted, disapproved or forbade. The Prophet's صلى الله عليه وسلم actions are considered an authority in Islamic law because the Muslims have been ordered to take him as their example. His tacit approvals are considered an authority in Islamic law because it would be right for the Prophet صلى الله عليه وسلم to remain silent in the presence of something wrong; hence, his silence implies his approval while his approval implies that the act is correct according to the Sharee'ah.
In this definition, the legal theorists have obviously excluded the Qur'aan from part of the definition - but the definition is inclusive of hadeeth qudsi. 
By referring to him as "the Prophet" صلى الله عليه وسلم they are thereby excluding what the Prophet صلى الله عليه وسلم said, did or approved of before he received revelation. Such would not be considered an authority in Islamic law.
Although "actions" of the Prophet صلى الله عليه وسلم is mentioned in the definition given above, in reality, the scholars of Islamic legal theory mean "selected actions" of the Prophet صلى الله عليه وسلم. That is, there are certain actions that are not considered as examples for others to follow. For example, it is narrated that the Prophet صلى الله عليه وسلم used to snore lightly. Note that the definition of the word "Sunnah" as given by the scholars of hadeeth would encompass this report as part of the Sunnah. However, since this act has no legal bearing - in the sense that no Muslim is requested to follow that act - it would not fall under the Islamic legal definition of the word Sunnah. 
Furthermore, there were some laws that were special for the Prophet صلى الله عليه وسلم only and that are not to be followed by the Muslims. An example of this type would be his marrying more than four wives. That was allowed for the Prophet صلى الله عليه وسلم and not for anyone after him. By the hadeeth scholars' definition, these would fall under the term "Sunnah," while, strictly speaking, it would not be a "Sunnah" in the legal theorists' point of view since no one is allowed to follow him in that action. 
 Hadeeth Qudsi are statements that the Prophet صلى الله عليه وسلم attributed to Allaah سبحانه و تعالى yet they do not form part of the Qur'aan. For example, they would include any hadeeth in which the Prophet صلى الله عليه وسلم said, "The Lord, Exalted and Perfect, said..."
For a detailed look at Hadeeth Qudsi, see: http://www.muftisays.com/forums/12-virtues/9570-hadithqudsi.html
 The above is not meant to imply that there are some acts of the Prophet that have no bearing whatsoever upon the Sharee'ah. Except for those laws specific to the Prophet alone, anything he did indicates, at the very least, that said act is permissible. There are some who try to divide the Prophet's Sunnah into what is meant to be part of the Sharee'ah and what is not meant to be part of the Sharee'ah. Unfortunately, many times this is done as a way to remove much of the Sunnah from the Sharee'ah. For a complete discussion and refutation of those claims, see Fathi Abdul Kareem, As-Sunnah: Tashreeh Laazim... Wa Daa'im (Maktabah Wahbah, 1985), passim.
 The Authority and Importance of the Sunnah, pp. 17-19