Difference between Have an interest in something and Have interests in something

have an interest in something—

1. be keen to know or learn about smth.:

• None of them had the slightest interest in music.

2. want smth. to be done:

• Governments have an interest in seeing minimum wages kept above subsistence level.

3. have a share in the ownership of a business:

• No resident of the Isle of Man is entitled to have an interest in the company.

have interests in something— = have an interest in something 3:

• The region obtains much of its oil from Alaska, where the combined group would have sizeable interests.