A label that varies by state
Embezzlement is defined in different words in different states, and some states, including New York, fold it into the general crime of larceny instead of charging it under its own name. Federal law has its own embezzlement provisions for particular settings, such as banks and federally funded programs. Because of that variety, the elements of embezzlement in your case depend on which law is charged, and a general description found online may not match. What these laws tend to share is a focus on someone who first had lawful access to property belonging to another and then treated it as their own. The wording that applies to you is something a lawyer should check against the actual charge.
Where the fight usually is
Most disputes do not center on whether money moved, because the records usually show that. They center on intent and on whose money it was. A person who believed a payment was authorized, earned, or a loan may not have acted with the intent the law requires, and the paper trail can help or hurt that account. Ownership questions come up in partnerships, family businesses, and joint accounts, where the line between one person's property and another's can be blurry. Repaying the money after being caught usually does not erase the offense, though it can matter in other ways.
Reading the charge against the facts
Once a charge or a demand letter exists, the useful work is to read it against the actual documents. We look at how your access was granted, what policies or agreements governed the money, how the amount was calculated, and what you have said so far. Value matters too, because it usually affects how serious the charge is. A first conversation is also where we discuss whether a civil claim is pending or likely and how that affects what you should say. Hold off on explaining the transactions to the employer, the family member, or the police until that review is done.