Using sub-resources, you get something like this: GET /orders/1/clients

So mapping this request onto a SQL database would be something like...

    SELECT * FROM orders WHERE client_id = 1

And for GET /clients/1/orders it seems like in practice it would be the same relation since it would be wasteful to store two tables. Is this roughly correct?

No. Think of it as "for order 1 list all clients", so it would be:

    SELECT * FROM clients WHERE client_id IN (SELECT client_id FROM orders WHERE order_id = @order_id)

The GET /clients/1/orders is what would result in your query (for client 1 list all orders).