Neither of these are good reasons to label a company a "startup." Arguably, Salesforce.com is 'still looking for a business model' despite being public, as are any number of other companies. And every tech company likes to think they have a culture of 'moving fast, raising capital and innovating.'

Wikipedia provides a reasonable starting place: "A startup company or startup is a company with a limited operating history. These companies, generally newly created, are in a phase of development and research for markets."