Not quite saying the same thing.
A petition is filed to USCIS who determines if the beneficiary meets the requirements; it's approved and sent to DOS. DOS interviews and verifies information is correct and true and then issues a visa. CBP determines admissibility - they ensure that the person attempting to enter the US has either a visa, permanent resident status or are a citizen, aren't bringing weapons and aren't a terrorist threat. CBP determine class of admission based on information provided by DOS in the case of people who require visas and verifying those documents aren't counterfeit. They should not be changing the class of admittance because they are there to enforce the law based on the information presented.
Have you ever heard of a CBP officer changing a non-immigrant visa to an immigrant class? Nope, because it's not within their jurisdiction of the law. There may well be some anecdotal cases of CBP admitting a CR-1 as an IR-1, but more often than not, CBP are going to go with what the DOS issued visa says. They can enforce what is in front of them. If the visa says CR-1, that's what they should admit on.
If CBP believe a permanent resident is in violation of the terms and conditions of their permanent residency, CBP may request the PR surrender their greencard, detain and/or issue a NTA, but they cannot take that PR away. Only an immigration judge can remove one's permanent resident status.
CBP screw up all the time, too. I've been incorrectly statused by CBP. I was admitted as a visitor, despite having a valid L-1. I had to find a deferred inspection site to get my I-94 fixed.
USCIS sent an CR-2 statused GC for Kid2. I had to send an I-90 to get it changed to an IR-2. Even funnier is they sent a notification to hubs to remember to remove conditions, despite having already issued the IR-2 greencard. So, clearly no communication.
No government agency scores a perfect 100. Too many communication silos and points of failure. Top of the list though, seems to be the SSA. Their own staff haven't read the application form for a SSN where it states a MRIV is proof of status. Many believe they need an actual greencard in hand to issue said SSN.