Symptoms of eczema and scabies can be very similar but they have very different causes: eczema is caused by an inflammatory reaction, whereas scabies is a mite infestation. For this reason, scabies is highly contagious through skin-to-skin contact.  As mentioned, eczema is not contagious.
Like eczema, scabies can produce an intensely itchy rash. In scabies, this rash can spread across the entire body, whereas in eczema, it tends to be localized to specific areas depending upon the type of eczema. In addition, a scabies rash often consists of redness with lots of small pimple-like lumps. You may also see subtle lines on the skin, where the mite has burrowed and laid eggs. It is common for mites to burrow between the toes and fingers.  Eczema rashes are highly variable but often involve dry, flaky skin.