Are there any differences between having dry skin and eczema?

Yes: People with eczema often complain that their skin is dry, but dry skin, in and of itself, is not the same as eczema. Treatments are completely different as well, so if you aren't sure what is going on, see a dermatologist.

Yes: Eczema is a form of hereditary dry skin that waxes and wanes and is more prominent in childhood. It is usually accompanied by cradle cap in infants and severe itching. Eczema has a particular pattern in the skin and it changes as you age, and mostly resolves in adolescence. People with eczema tend to have allergic problems.

Different in degree: Dry skin just dry and flaky. It becomes "eczema" when it's itchy, red, oozy, crusted, blistering, swollen, etc.