A charge card is American Express Green, Gold, Platinum, Centurion and (perhaps, but I'm not positive) Plum. It has no preset spending limit but AMEX carefully watches your activity and can deny any charge at any time. I am renovating my house and called and told them my spend would be much more than usual on my Plat personal AMEX but same on my business Plum card: $65K a month for 8 months. They said no problem. Three months in, I was at Chipotle and they denied the $8 burrito, got a call that second on my phone and it took 5 minutes for them to approve it (I had already paid with my Chase Sapphire Preferred visa card). The rep just said it was account management dept and couldn't really give me any details. It was annoying; their evasiveness really pissed me off. I then was told I was up for a financial review. I have been a cardmember, according to my card, since 1985. I had to send in mountains of paperwork from the IRS, my bank, my brokerage accounts and estate attorney before they would let me touch my AMEX MR's or any AMEX cards (personal or business). I was pissed. After the FR was over, the rep had the gall to ask me if I wanted to be a Centurion member again. I was unwilling to give up the 2.8M MR points I had, so I complied, but once my account was lifted, I drained my MRs. Once Costco's relationship ends with AMEX, I will be cancelling my Plum and Plat card. 95% of my spend is now on CSP and I've had no complaints (plus it is nice to know what my actual credit limit is rather than it being at AMEX's will...although I know Chase could deny any charge too, I like the transparency Chase offers).
In short: Charge cards are a few of the American Express cards that do not have a preset spending limit and are due in net 30 terms unless previously arranged for a longer due date (although this option is very expensive). They tend to be marketed towards the affluent, wealthy individuals and businesses. They used to be more popular but since the 90s, have fallen out of favor, except from the top 0.5%. Since post financial crisis, Chase and Citi have aggressively gone after AMEX customers and with AMEX losing its exclusivity agreement with Costco, I don't see good days to come for AMEX (something like 25% of total volume of all AMEX transactions was at Costco).