I'm learning about 鲁迅 and the picture he saw of a man being decapitated.
My teacher would switch between 杀头 and 砍头 - is their a large difference between the two? is one more formal? Is there a difference in usage?
Sorry for being a bit morbid - but this is helpful!
殺頭 is a kind of dead sentence (/punishment) carried out by government officials.
砍頭 is a way to kill people.
e.g. if it is "victim vs gangsters", you can only say "砍頭" but not "殺頭".
But when used as adjectives ("殺頭的" and "砍頭的"), it is okay to switched between them, as said by Opteron and user3306356.
杀头 = be sentenced to death
砍头 = be beheaded
In the old times, death penalty is carried out by beheading, so it is OK to switch between the two words.
砍头 is concrete. It invokes the image of hacking with an axe or sword. When it is done with a piano wire, this word is definitely not a good choice.
砍，读kǎn，用刀斧等猛剁，用力劈：～柴。～伐。 chop；chop at；hack；hew；shear. Like chopping wood with an axe.
source: http://baike.baidu.com/view/264052.htm?fr=aladdin
杀头 is generic and abstract. It does not invoke particular image.
杀, 使失去生命. To cause living thing to lose life.
砍头is the official expression 杀头 is the civil expression
杀头 means to kill a prisoner, the prisoner can be killed by a gun, or lethal injection. While 砍头 means decapitation only.
