diversify/branch out

Hello,
When we talk about businesses providing more services or different goods, can we use both? I usually see diversify. Examples: "The company has branched out into providing investment advice." "Farmers are encouraged to diversify into new crops." Here's my take which is probably wrong: When we branch out into something, we start making new things, but we don't stop making the old ones. With diversify, we stop making/producing/growing/etc something, in order to produce/grow/make/ something else.

Thank you