It depends on the state and the violation.
Some violations upon conviction that are considered serious or major will result in suspension of your CDL regardless of how many points you have. There is no longer any distinction between getting a violation in your car or in a big truck for CDL holders.
For minor moving violations it depends on your state, and sometimes the state you are convicted in, as to how many points you can rack up before being suspended. And yes you can have your driving privledges suspended in one state and not in another.
Quote:
Serious traffic violation means conviction of any of the following offenses when operating a CMV, except weight, defect and parking violations:
(a) Excessive speeding, involving any single offense for any speed of 15 miles per hour or more above the posted speed limit;
(b) Reckless driving, as defined by State or local law or regulation, including but not limited to offenses of driving a CMV in willful or wanton disregard for the safety of persons or property;
(c) Improper or erratic traffic lane changes;
(d) Following the vehicle ahead too closely;
(e) A violation, arising in connection with a fatal accident, of State or local law relating to motor vehicle traffic control;
(f) Driving a CMV without obtaining a CDL;
(g) Driving a CMV without a CDL in the driver's possession. Any individual who provides proof to the enforcement authority that issued the citation, by the date the individual must appear in court or pay any fine for such a violation, that the individual held a valid CDL on the date the citation was issued, shall not be guilty of this offense; or
(h) Driving a CMV without the proper class of CDL and/or endorsements for the specific vehicle group being operated or for the passengers or type of cargo being transported.
2 convictions of the above in a 3 year period is a minimum of a 60 day suspension. 3 in 3 years is a minimum of 120 days suspension.
Major offenses will result in a suspension of anywhere from 1 year to lifetime.
LIST OF MAJORS AND PENALTIES 
