They can happen in either order.

In New York State, you can be arrested for a felony without an indictment, if the police have probable cause to believe you committed a crime. The charging document is called a Felony Complaint. After the arrest, unless a disposition can be worked out between the DA's office and the defense (such as a guilty plea or reduced charges), the only way for the case to proceed to trial is via indictment. You cannot go to trial in New York on a Felony Complaint.

Alternatively, if a felony is committed, the DA's office can choose to present evidence to the Grand Jury and secure an indictment before the target is arrested, it's known as a De Novo indictment. After the indictment is secured, the defendant is arrested and arraigned on the indictment and the case proceeds exactly the same as if the defendant had already been arrested on a felony complaint.