You can use the standard CSS comma to define a group selector:
$('#next_step, #design_next_step').on('submit click', function(){ ... });
When you click a button or link to a link ...
But the buttons are not sent, they are pressed. The submit event is for form elements, not button or input elements. Assuming you have specified id for elements that are buttons or links, just use the click event:
$('#next_step, #design_next_step').on('click', function(){ ... });
Depending on what you are doing, you may or may not want to prevent the default action for the event [by accepting the event argument and calling preventDefault on it or doing return false in a handler that will prevent the default propagation and stop propagating]. The default action for click in links is, for example, a link to a link.
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