Is heart scan same as the CT scan?

Yes.

Newer name for the same thing:

• CT is 'computed tomography'
• CAT was 'computed axial tomography'

Both use a narrow x-ray beam rotated about the axis of the object being scanned (thus the Word "axial" in the original name), a powerful computer is then used to reduce the information collected to produce a special photo called a "tomograph". No difference at all other than the name was shortened.