Yes, basically they're nearly identical. Technically, though, a stay in an intermittent city under 24 hours is a layover. Any minute over, and it's a stopover. That's for international flights. For domestic trips, a stopover is anything over 4 hours.
And while it may not seem like a big difference, flights with stopovers can often allow you to stay for multiple days in the connecting city at a free or discounted charge (there is a time limit, though). It all basically depends on the fare rules when you book your ticket.
Generally, the rule is that the more you paid for your ticket, the greater the likelihood of having a free stopover. That's something that'd you have to check with your travel agent or airline puppetmaster, though.