Both forms can legally cover a fourplex, and they price and pay differently, which is why your two people disagree. The dwelling route is usually a landlord policy (agents often say DP3 or dwelling fire) written per building, covering the structure, your liability as owner, and loss of rents if the units are unrentable after a covered loss. Commercial package policies are built for portfolios and mixed use and tend to carry higher minimum premiums for a single small building, though they're more flexible on unusual risks.
Lenders on 2-4 unit residential loans generally want a form they recognize, with replacement cost on the dwelling and a rent loss amount tied to your gross rents. If the policy language doesn't match what their checklist expects, the file stalls at closing. So ask the agent to quote both and ask the loan officer to send her insurance requirements in writing, then compare.
Two coverages worth naming while you're shopping, since fourplexes are often older buildings: ordinance and law coverage, which pays the extra cost of rebuilding to current code after a loss, and enough rent loss months to survive a long repair. Also confirm the tenants carry renters insurance and that your lease requires it.
Managing property you own yourself doesn't require a real estate or property management license in most states. Managing units for someone else usually does. That's a state-by-state rule, so check your state's real estate commission before you take on a friend's duplex.