What are the intentions of the different forms of Armature/Bone Parent/Child relationships? Hello to every blender user,

AFAIK I can parent a bone to a part of the mesh (in the specific case the teeth.t bone and the upper_teeth_boy) in two ways :

1) I go under the object tab and I chose rig.boy on the parent field and teeth.T bone under the bone field. But it didn't work,because the upper_teeth_boy takes a strange angle

2) instead,if I select the upper_teeth_boy first and teeth.T for second and then I press CTRL P and then set parent to bone,it works.

In the attached video,I have parented upper_teeth_boy and teeth.T using the procedure explained on point 2) and then I removed the parent and I did the same but using the procedure explained on the point 1) but it didn't work. Why ? Thanks.

demonstration video 1

blender file

I didn't use the "Keep transform" option. This behaviour appears also if parent has default loc/rot/scale,as you can see from this video : demonstration video 2
Parent Child Relationship and Keep Transform




There are different ways to create a Parent/Child relationship in Blender or parent.  
Keep Transform stealthily does the appropriate math with matrices to preserve child placement.
Some ways have [immediate] effect in placement, others (Keep Transform) [delayed].







In the two object parent and armature parent menus above we see (Keep Transform) as a valuable option.
The [Keep Transform] genre intentionally preserve child placement at the time of parent assignment, then you move the Parent for different results.  
You should choose the one the best suits your context.  If the [immediate] effect is not what you want today, then the suggestion is to view it as a feature that you may use in the future for a positive Blender User experience.
Both parent menus above have many different options so you may expect this as a feature.  All of those options may be useful to Blender Users in some particular cases.
Via Control-P use Keep Transform for the case in question.  Manually filling in Parent does not necessarily [Keep Transform].  If the parent has any (non default) Scale, Rotations, or Translation the new Child will be transformed accordingly.  Expect this designed behavior.  It is a feature not a defect.
This was intended as a short explanation.  See more here at BSE or the online Blender Manual