I have a Challenger panel board and one of my breakers is no good. When I went to buy a new one they don't carry them anymore. They said they only carry the after-market ones. So I got that one, but it looks different than the original one. Will it fit in even though it's a different looking one?
You can use BRs instead of Cs
If your panel labeling says it takes type C breakers, then there's an easy way out of it: type BR breakers (as depicted below, with the type C labeling highlighted) are legal, safe, and widely-available (at any big-box or hardware store) replacements for type C breakers, as they are cross-listed (as per this letter from UL to Cutler-Hammer, as reproduced at the bottom of this post) and cross-labeled to replace type C breakers. (A more modern version of this letter is available, linked from an Eaton FAQ.)
For more exotic Challenger breaker types, Eaton cross-reference document TD01201041E provides the gory details.
"But I have those weird 'thin' breakers with the half clips, that have two genders, and allow a thin 2-pole to sit between them".
I have a feeling those are not actually certified for that brand of panel, but I could be wrong.
Today, The weird little "thin" breakers with their alternating side clips are obsolete, and I don't think they made them in 60A anyway (too much for that dainty little bus clip). Today, you use tandem or quadplex breakers such as Eaton BRD, BD or BQ breakers. A tandem is two of those "thins". A quadplex is two singles with a 2-pole in the middle. Both factory-made together with approved bus clips for that panel.
Yes, you should have no trouble finding up to 50A in a quadplex. (60A is a no-go, sorry, but nobody needs 60A for EV charging. Nobody who drives 400 miles a day everyday buys an EV expecting to charge at home.)
It will likely fit & you probably won't have any problems. But, read the panel's door for specifics of a replacement. Some panels are very particular about what materials or brands of breakers go in.
If there's no mention of "only these brands", then whatever fits securely will be fine...they all have to meet the same standards, looks don't mean anything to electricity.