Maya: Introduction

World vs Object Translation

https://knowledge.autodesk.com/support/maya/learn-explore/caas/CloudHelp/cloudhelp/2018/ENU/Maya-Basics/files/GUID-A63AC5C8-8822-42AC-827E-164B5266DA03-htm.html

World
World space is a coordinated system in the representation of the World space, which has its original at the centre of the scene view. The movement will be based on the X, Y and Z axes. When an object is moved, the World space and axis will be aligned to our previous location.

Object
Object space is a coordinated system based on the object's perspective rather than the entire scene. The origin of the object is the pivot point of that particular object. The axes of the object are rotated with the object itself.

There is also the option to have Local space, which can be used when you have an object containing child objects in the hierarchy. The local space will use the origin and axes of the parent only, but apply to the entire group.

By clicking on the object, then double-clicking the highlighted tool on the left hand panel the Tool Settings can be accessed. Through the menu we can change the axis orientation and various other settings.