Michael Cohen arranged the NDA and payment to Stormy Daniels through a shell corporation he set up. Trump reimbursed Cohen for the payments which the Trump Organization documented as "legal services". Cohen was paid a bonus and the total amount of the reimbursement was "grossed up" to make his reimbursement whole after taxes. Cohen was charged with violating federal campaign finance laws in relation to the payments as it was considered to be an illegal and unreported contribution to Trump's 2016 presidential campaign.
The path they're taking is that the documentation of the payments was a falsification of business records as the reimbursement to Cohen wasn't a "legal service" to the Trump Organization but a contribution to Donald Trump’s campaign and/or personal expense of Donald Trump.
The falsification of business records is a misdemeanor in New York with a statute of limitation of 2 years. However, falsification of business records with the intent to cover up a crime can be charged as a felony in New York. In this case, the underlying crime would have been Cohen's campaign finance violation as he's plead guilty to it. So the felony charge would be a falsification of business records to cover up a federal campaign finance violation.
The statue of limitations there is 5 years. Trump's final reimbursement to Cohen came in December of 2017 but accounting for the payments may have carried into 2018 which would still put us barely into the SoL window which is why they're moving on it now.
Bragg would need to verifably document records on the payments into 2018 and if he's successful there, he'll need to prove that Trump acted with INTENT to cover up the commission of campaign finance violations which will be difficult to say the least as Trumps likely defense will be his intent was to prevent personal and reputational damage.
This is what it is all about. Other legal minds can weigh in on whether this would ever be pursued in any other instance. I already know the answer. Like the guy, or hate the guy, this to me is absolutely silly, and also very obvious in intent. It shows lack of prosecutorial judgment, and probably leads to prosecutorial misconduct. But that's where we're at I guess.