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I will try to catch this one... 

Let's start by the TCP, it is the Tool Center Point.
This parameter is available inside the installation tab.
It is specific to a tool or a reference related to the tool. 
It represents a translation and reorientation from the end of the robot (Robot wrist flange). 
This is a variable that you set to a value to represent the tool (numerically speaking). 
You can move along axes matching the TCP orientation. This in the range of the work envelope.
You can rotate around the TCP and around the TCP axis in the tool mode to reorient the tooling in the space. 
It shall be set by a human or using a definition procedure. 
It is used to adjust between tool change or tool length variation.  

The TCP is the numeric reference you send to a waypoint. 
It is rare a single TCP is changed or will change by itself. 
Usually, we use a new TCP reference (with Its own name) for new tools. 
You always have one, the undefined default one being at 0 translation and 0 rotation. 

If it fluctuates, it is probably the position in the space of the TCP, alike the waypoint. 
Waypoint or current position in the space is given relative to a reference. 
Usually the reference is the center of the base. 
Waypoints are built of a translation from the reference and an orientation using 3 parameters. 

Here is the interesting part for sign change. Orientation being given by 3 parameters, it can be possible to have 2 set of values representing the same place. 
The other possibility would be that the robot tilt a little to pass near a singularity from "-2.2" degree to "2.2" degree. 
The last possibility is that the robot is a UR3e and all UR3 have the last axis able to turn without limit. 

Hope this helps you.