Strictly speaking, a shandy is a mix of beer and lemonade or some kind of lemon soda or soft drink, which is preferably carbonated. Meanwhile, a radler is more flexible.
While you can make a radler with lemon soda, it can also be mixed with other juices. However, both a shandy and a radler will typically be made with a lighter beer.
The divergence between shandies and radlers is not only in their ingredients but also in their origins. The shandy has British roots, while the radler hails from Germany.