Are immigration and naturalization two separate things? Is the federal government usurping a power not delegated to it by the Constitution?

I think it can be reasonably argued that the power to regulate immigration, and the power to regulate naturalization are two separate powers. 

The Constitution clearly delegates naturalization to The Congress. Article 1 section 8 delegates to Congress the power to "establish universal rules for naturalization" 

The Constitution is silent on immigration. This,  as affirmed by the 10th amendment would mean that the States retain their power to regulate immigration.

If state law is silent then that power is retained by the people of each state through private property rights. 

Perhaps this separation of powers is part of the checks and balances the framers intended. States control immigration deciding who can live and work in their state, Federal government decides who is naturalized as a permanent resident or citizen. 

Edit: The naturalization act of 1790 does not appear to regulate immigration at all. 

The federal government holds the sole power to set immigration policy; eg who can enter, reside, and become a citizen. Homeland Security, ICE, and US Citizenship and Immigration (USCIS) et al. Any state and/or local laws that have attempted to regulate immigration have generally been preempted / invalidated by federal law in part due to the Supremacy Clause of  the constitution. States can and do certainly pass legislation that greatly influence and affect immigrant's existence.

Immigration and naturalization are two different processes as you suggest, with the former involving the move of immigrants into the country/ settlement and the latter denoting the attainment of the US citizenship process.

Then from what clause of the Constitution does the federal government claim the authority to regulate immigration?

I think that practice, custom, and the general opinion of the people say that the federal government should control immigration. All the legal poop aside, if one state's immigration policies were strict and another's lax, immigrants could enter the strict state via the lax state, as interstate borders aren't controlled. Thus, actual immigration policy, from a practical standpoint, would be that of the most lax state.

I'm not saying whether "lax" or "strict" or desirable. I'm just pointing out the impossibility of delegating this power to the states. FWIW, I think we should have a very lax immigration/work/residency policy, since we need labor as our workforce ages. I think we should have a fairly strict naturalization policy.

True, state borders are generally not controlled, however State territory and jurisdiction is. States could have laws that control how and when immigrants can work, how and when immigrants can receive state identification, how and when immigrants are able to drive vehicles, when detaining someone for another crime and finding out they are "illegal", they could remove them from the state. There are several ways the states could enforce their own immigration policies. 

Side note: I too am generally in favor of the easy to visit/live/work but more difficult to become a citizen approach. 

 @LiveFreeNW...

I had to look this up, so please remit $39.99 once you recover from Christmas expenses..

From Cornell Law School Legal Information Institute :

"Federal control over immigration stems from congressional implied plenary power as a sovereign nation. That power is derived from inherent authorities and clauses such as the Necessary and Proper Clause (Art.1, section 8), the Naturalization Clause ( Art.1. section 8), and the Foreign Commerce Clause. All of those references are reinforced by the Supremacy Clause (Art.VI). "

https:// www.law.cornell.edu/constitution-conan/article-I/section-8/clause-18/implied-power-of-congress-over-immigration-overview

I'll send you a Trump Bible instead. Autographed by JD Vance, with a beautiful drawing of a Haitian gnawing on a dead cat on the inside cover. Far more valuable.

I can't help but observe that when Abbott the Bunny Rabbit deployed the Texas National Guard to the border, both when he tried to dunk booby traps in the Rio Grande and when he had them stop and search every truck coming north, he was in violation of the federal laws that you cite. He of course faced no consequences for that.

Actually, he stood on some other constitutional tenets to argue against his border problems , though SCOTUS kinda gave him a bittersweet ending to his stances and shifted it off to the appeals courts. To my knoiwledge those aren't all settled as yet but they have less importance under today's conditions. Abbott and Texas took it in the shorts after some of the appeals court rulings.

However, I'm willing and able to  look up those constitutional references he claimed in his arguments but it'll be pricey.

Don't bother. I know that Abbott was full of shit when he claimed jurisdiction over the border. It's like when I see a pile of dog crap on the lawn, I don't need forensics to prove that a dog did it.

I wasn't looking forward to it anyway..so we can all remain ignorant with the related bliss of his employed tenets. I'm speculating / spitballing here but, I'll bet a majority of Texas citizen voters approve of his border actions in the next gubernatorial election ( for his fourth term). The real answer to that will come next November , as there are no term limits for Texas governors. You've already written off Texas/Texans so don't concern yourself , Inspector.