Description of the error and steps
It takes one extra click on each case to change selection between an object and bone and viceversa.
In 2.8, with Lock Object Modes turned off, this scenario takes 6 Clicks in total. It works like this:
-One click on BoneA puts you into Pose mode, but if another bone was selected you have to click on BoneA again. From Pose mode, one click on an Object puts you into Object mode, but it doesn't select the objecet, the armature is selected instead, so you have to click the object again. Now click on BoneB and youll be back in pose mode, except BoneA will be selected from your last time in pose mode, so you need an extra click. *
In 2.79 the same scenario takes 3 Clicks in total. It worked like this:
-From Object mode, one click on BoneA selects BoneA putting you into Pose mode directly, one click on an Object selects that object alone and puts you in back Object mode, a click on BoneB selects BoneB, and only BoneB, not the previously selected BoneA, and puts you into Pose mode again.
Try it with this file in 2.79 and then in 2.8