Intersex
This is the definition for people born with physical sexual or reproductive qualities (which include chromosomes and hormones) that do not fit into the binary male/female distinctions. In intersex cases, the biological sex of a person is ambiguous.

Transgender
Being transgender means that there is a mismatch between the sex you were assigned at birth and your gender identity. For example, in the case of transgender women – they would have been assigned as male when they were born for displaying the physiological characteristics that are typically male but may identify as female in terms of how they see themselves within the social constructs of the world.

It is possible to be both intersex and transgender, but they are not the same thing. Intersex relates to a physiological designation – which sex a person is assigned based on the physiological traits they display – while being transgender is about how someone expresses their gender identity.