Assumable Mortgage Scenario (Explain like I'm 5)

[Kendric Buford]

I've been trying to wrap my head around assumable mortgages, but I'm not sure I get it fully. Can someone tell me if this scenario is accurate, or explain it like I'm a child?
Scenario: (using round numbers so I can follow better)
Seller is trying to sell their house for $300,000 but can't. Their Original Purchase Price was $250,000 at 3%. They currently have $50,000 in equity in the property. I offer to buy it by assuming their mortgage. Does that mean I'd take over the remaining loan of $200,000 at 3%, then I'd have to pay the seller $50,000 for their current equity, and an additional $50,000 to cover the difference from the initial amount they wanted to sell for ($300,000)? - Also, I presume this is where my cash and/or a second mortgage would come in, so I can pay the seller.

**To keep things as simple as possible, I didn't mention any closing costs or commission to an agent for this scenario.  

So at the end of all this, if I'm understanding correctly, the Seller would walk away with the $100,000 that they would have from a normal sale, but I get a 3% mortgage rate and the property?