It seems that if I fly withing the USA, then there is no limit on what I can carry currency wise but when leaving the USA, I am limited to under $10,000.
Is this correct or not?
Not quite correct. There is no law in the U.S. that restricts the amount of cash you may carry while traveling, whether it is travel entirely within the U.S. or whether you are going into or out of the U.S. However, a number of other nations do have currency restrictions of some kind, and you'd want to ensure that you understand those laws before traveling to those countries.
What U.S. law does provide is that if you transport into or out of the U.S. more than $10,000 in currency you must report that transaction to CBP using Fin Cen Form 105. Failure to comply with this provision may result in seizure and forfeiture of the cash as well as a fine of up to $500,000 and/or 10 years in federal prison. Depending on the circumstances, other reporting might also be required.
You raised the issue of transporting cash to Puerto Rico. Puerto Rico is a territory of the U.S. The law imposing the reporting requirement is 31 U.S.C. § 5313. The definitions that apply to that law are found in 31 U.S.C. § 5312. United States is defined in § 5312(a)(6) to mean “the States of the United States, the District of Columbia, and, when the Secretary prescribes by regulation, the Commonwealth of Puerto Rico, the Virgin Islands, Guam, the Northern Mariana Islands, American Samoa, the Trust Territory of the Pacific Islands, a territory or possession of the United States, or a military or diplomatic establishment.”
So, in order to determine if Puerto Rico is considered part of the U.S. for this purpose (and thus whether reporting is required), one must look at the Treasury Regulations on the subject, found in Title 31 of the Code of Federal Regulations (CFR), Chapter X. Specifically, 31 CFR § 1010.100(hhh) defines United States as follows: “The States of the United States, the District of Columbia, the Indian lands (as that term is defined in the Indian Gaming Regulatory Act), and the Territories and Insular Possessions of the United States.” So, it appears that transporting over $10,000 in cash from a U.S. state to Puerto Rico should be treated just like transporting it from one U.S. state to another for the purpose of determining the obligation to file Fin Cen Form 105.
Note that the obligation to file the Fin Cen Form 105 does not depend how the cash is transported, so whether by commercial flight, by private jet, by boat, through the mail, or whatever, the requirement will apply.
Note that for other purposes, notably income tax laws, Puerto Rico is treated like a foreign country. Thus, you have to look at each particular law at issue to see how Puerto Rico (or any other territory or possession) is treated. For some purposes, it is treated as though a part of the U.S., and for others as though it is not.