What is Aadhaar smart card or plastic card? Is it mandatory for getting services?

There is no concept such as smart Aadhaar card. Aadhaar letter or Aadhaar downloaded from UIDAI website, in the form as may be specified from time to time, is sufficient and a valid form of Aadhaar. Only visit authorized common service centres or Aadhaar permanent enrolment centres for Aadhaar related services. For further info see this press release: https://goo.gl/TccM9f.