charge someone with something
1. to place criminal charges against someone. The police charged Max with robbery.
2. to order someone to do a particular task. The president charged him with organizing the meeting. We charged her with locating new office space.
accuse someone of something to charge someone with a crime, a violation of rules or instructions, or doing something wrong. Please don't accuse me of forgetting to lock the door.
So far as I understand it, the main difference between them is that "charge ..." is used when a criminal incident is involved. Accusing someone of something can also refer to a simple mistake, as mentioned in the example "forgetting to lock the door", which of course isn't criminal or against the law.