The deal is done with a handshake and the site is up in less than a month. Of course not. If there was no contract, or if the underlying contract between you and your website developer does not clearly indicate that you own the text, designs and scripts, then the developer may be free to use any part of the website for any other competitor. Copyright protection is automatic after setting pen to paper or keystroke to computer, but copyright registration can provide additional protections. Trademark registration is critical to protect certain text and designs.
Patent law covers specific and well-delineated ideas for physical objects.
Some software may incorporate certain functions that could qualify it for patent protection as a business method patents. No business would want to give this intellectual property away, yet many do. This can be a standalone agreement or part of a larger contract. NDAs are commonly used in the technology and Internet startup world to protect intellectual property. Often drafted as part of a nondisclosure agreement, it too can be a separate agreement or part of a more comprehensive contract.