A WOSB certification is different from a WBE certification. The WOSB certification is a federal program administered by the SBA, while WBE (Women's Business Enterprise) is typically a state or local certification. My firm holds both a federal WOSB certification and statewide term contracts in Georgia, and they are distinct processes.
For federal contracting, the SBA certifies a firm as a WOSB for specific NAICS codes. A WOSB sole-source award requires an SBA-certified concern and an anticipated price, including options, not exceeding $8.5 million for manufacturing NAICS codes or $5.5 million for any other NAICS code (FAR 19.1506(c) and (d)).
WBE certifications are generally handled by state or city agencies, or by third-party organizations recognized by those jurisdictions. There is no single national WBE certificate; it is usually specific to the entity requiring it. For example, my state of Georgia has a specific state procurement portal and a vendor registration process for its statewide term contracts. The paperwork you completed for your WOSB certification will provide a good foundation for a WBE application. Many of the ownership and control documents will be similar, but you will still need to follow the specific application process for the city or state you are targeting.