How is software defined networking different from VLANs?

Tomas summarized it perfectly with his simplistic answer. 

Software Defined Networking is a concept when you define your networks, routes, firewalls, ... on a software level ("anything as a code") rather than via traditional means. It's common in cloud environment – and similar to how you would set up e.g. virtual instances, drives & storages, etc. using source code / scripts / tools rather than "by plugging cables and powering up machines".

VLAN is, simply put, a mechanism how to make network devices in different physical networks "feel as though they were in the same LAN". 

A slightly simplistic answer to your question is that "you can use software-defined networking to define and manage your VLANs" ...