For audio.
Generally in time mode all stays as it is, only grid change.
In beats/position mode items start follow grid.
In beats/position/rate mode items start follow grid but also items are stretched.
For midi:
in all modes items adapt to grid when tempo change.
ps. set in project settings your desired mode. To make it default in every new project:
1.open new project
2.go to project settings and set as you want
3.save project as template
4.go to Preferences\Project, browse for your project template
Now every new project will follow settings from your default template, I recommend to set such default project to keep you settings on new projects because some settings like in mixer, metronome etc. arent keep on new project (are project dependent) so when you set something and open new project without your default template you will have to set those in each new project.