What is the distinction between ordinance types in the LDS church? I recently listened to a discussion between a couple of LDS leaders in which there was a clear distinction drawn between "priesthood ordinances" and "temple ordinances". Baptism, at least, seemed to be of the former sort, but it wasn't clear what the other ordinances were or why there were two types.

What is the difference between these two types of ordinances and where did the distinction originate?
Priesthood ordinances are any ordinances performed by the Priesthood authority. Temple ordinances are only those ordinances performed in the temples. All ordinances are performed by the authority of the Priesthood, though, so I think the phrase "priesthood ordinances" is just used for emphasis or clarity. Either that, or "priesthood ordinances" might also refer to those ordinances directly involving the priesthood, such as conferring it to another man or ordaining to a particular office. 

In the general sense, temple ordinances are a subset of priesthood ordinances.

There are many ordinances in the LDS Church performed by this authority, here are a few:


Baptism
Laying on of hands to confer the gift of the Holy Ghost (known as "confirmation")
Laying on of hands to confer the priesthood
Temple ordinances, which includes, among several, endowments and sealings (eternal marriages)
The Sacrament (administered every Sunday in church)
Consecrating oil used for...
...laying on of hands to bless the sick and afflicted
Giving blessings of comfort/counsel
Setting apart church members for their respective callings in the Church, including missionaries
Dedicating/consecrating buildings
Dedicating graves
Giving new babies in the church a name and a blessing (like a typical Christening in other churches)
Patriarchal blessings


This may naturally lead to the question, are there any ordinances performed not by the priesthood? No, not in the LDS Church. Maybe the word has different meanings elsewhere, but most commonly among the Latter-day Saints, it is a term referring directly to exercising the priesthood authority.

From lds.org:


  "Priesthood is the authority and the power which God has granted to men on earth to act for Him. When priesthood authority is exercised properly, priesthood bearers do what He would do if He were present."
  
  —President Boyd K. Packer


Here is a more comprehensive summary of the most common ordinances in the LDS church.