I recommend you get both if cost is not a consideration. Normally the certificate is needed and issued because you were born outside the United States to a US citizen parent or because you automatically became a citizen of the United States after birth but before you turned 18 years old.
US Citizenship and Immigration Services issues the Certificate of Citizenship. As of this writing the fee is several hundred dollars. It will take several months to have the certificate issued and you cannot use the certificate to travel internationally and return to the United States. However, it is definitive proof that you are a US citizen without anything else and the certificate does not expire.
The US Department of State issues the US passport. The fee for the passport is less expensive than for the Certificate of Citizenship. The passport can also be issued much more quickly. The passport must be renewed every 5 to 10 years depending on your age. If you are a US citizen planning to travel internationally, you must have a US passport when returning to the United States. The US passport is definitive proof that you are a US citizen even if you do not have a Certificate of Citizenship.
If you have any questions regarding US citizenship, please feel free to call me, attorney Shawn Mesa at (813) 679-5780.
Disclaimer: This information is provided as a public service and not intended to establish an attorney-client relationship. Any reliance on this information is taken at your own risk.