When talking about the Christmas Truce, it is more accurate to refer to it in plural. There were many truces along the Western Front during the Christmas of 1914, but the truce(s) was/were not total. Shelling and firing continued in some parts and there were deaths on Christmas Day. Some of the truces had been arranged on Christmas Eve while others were arranged on Christmas Day, and as such there were flare-ups depending on the timing of the particular truce in question. When they did happen, the precise conditions of the truce varied. In some cases there was actual fraternizing and an exchange of various pleasantries, while in the others the "truce" was limited to a brief respite for the explicit purpose of recovering the bodies of the dead with an uneasy "do not fire unless fired upon" atmosphere.

Some of the would-be fraternizers were shot by snipers who were either unaware of the (entirely unofficial) truce, or were specifically ordered to fire upon the enemy troops, while some were killed or injured by the artillery (which, due to being situated behind the trench lines, was unlikely to have been informed of the unofficial truce, or unwilling to partake in it).

Similar truces flared up during the later years, but by then the war was already well underway and there was little appetite for fraternizing, so all of the subsequent ones were highly localized and extremely brief. Specifically, for example, during the Christmas of 1916 some elements of Princess Patricia's Canadian Light Infantry exchanged some souvenirs with the German troops, but their neighbours from the Royal 22nd Regiment (known as "Van Doos") proceeded to raid the German trenches, allegedly stealing their presents in the process.

To expand a little on the previous response, you might find this old answer to be of interest as I make note of several incidents of combat.