I don’t think PSA and CGC are objectively similar. Their grading scales are not the same. Their grading standards of what’s accepted are not the same. If anything cgc has more in common with bgs. That was their primary target when they launched.
As for the original topic, I completely avoid this noise. I auction hundreds of cards each month through fanatics from 0xx certs to the newest and never even think about this topic whatsoever. I really think this is a major in the weeds situation.
CRC is not a “service.” It’s a customer service mechanism to potentially ‘dispute’ a PSA grade/slab attribute, inconsistency, etc. with a pathway to escalation. It’s something that you have to reach out to PSA for and if they agree it’s applicable to your case will provide you with instructions on how to send in your card and proceed.
There is more context to that Charizard receiving a new cert number that the person who had it done has left out. PSA will absolutely not change a card’s cert number for the vast majority of cases, so something else was an ‘issue’ with this card.
The more likely scenario is the person who sent it in was not the original owner, claimed the card may be inauthentic and PSA agreed to let them send it in through CRC on the condition that it needed to be fully regraded before being reslabbed and that is what happened. If a card is agreed to go through a full regrade process then it is always assigned a new cert number.
That makes a lot more sense! Thanks!
… and he charges a lot I would assume for that sticker and his personal opinion on your graded card lol Seems silly to pay extra for someone saying your grade is great here’s a gold sticker
Can we keep on topic, please? 
Good to finally know the reason why my legitimate CRC requests are getting clogged up for weeks 