Currently, there are 2 different wrenches from Industrial Craft and BuildCraft. There is also a Forestry wrench, but Forestry is not included in the current recommended build of technic. Each wrench serves a different set of functions.
NOTE: Industrial Craft wrenches do not pick up BuildCraft machinery and vice versa.
Industrial Craft WrenchEdit
The Industrial Craft wrench can be used to pick up machines and reorient some of the machines. In order to so, perform a right-click on the machine you want to pick up. Take note that you should remove a machine only when it is absolutely necessary since there is a chance that you just get a Machine Block instead of the machine itself. This can be avoided by making an electric wrench, which has a lossless mode.
NOTE: Forestry is not in the current recommended build of technic. The Forestry wrench can be used to reorient Biogas engines and peat-fired engines. Those engines will try to orient themselves to the next available powerable machine on initial placement. Sometimes you will have to reorient it towards the machine it should power. Use a wrench to do so. Forestry will also use (in that order) the BuildCraft wrench or the IndustrialCraft wrench depending on which mods are present. As both the BuildCraft and the IndustrialCraft wrenches are present in the Technic Pack, it is not necessary to craft the Forestry wrench.