There was a part of Texas which was considered to be "no mans land". For what ever reason, Mexico and U.S decided in the compromise of 1850, they would have a zone in Texas which neither of them ruled...... this was an area where people were literally set free, it was public land.

Their attempt to attract settlers was much more successful than predicted, Texas had so much land it was literally dirt cheap, there was little to no law enforcement. They screwed up telling the settlers they weren't under Mexican rule. There were wonky and unclear rules established on Texians. So when Santa Anna rolls around with his boys telling the settlers they aren't abiding by Mexican law and they should reform to Catholicism, they revolt and claim they were never forced to do this before.

It gets rough, the Texians creates a committee which is horribly unprofessional, they go between a nut job who lost the Texas navy and a few volunteer army’s trying to fight against Anna while Austin is trying to get things done the political way.

Eventually Tejanos and Texians get their independence but it was self proclaimed, they fought it out with Mexico and struggled for a few years while being an independent state. It was convenient that the Mexican revolution was taking place against their crumbling Spaniard rule.

I highly recommend Gone to Texas, a really great read. Begins with the native nomadic settlers many years ago, taking you all the way through Texas history

I can understand why you would have that impression, but there are a few more steps in there.

The Texas residents (including people of Spanish/Mexican heritage and newer arrivals dominated by former US residents) of what is now Texas revolted against the new military dictatorship of Santa Anna in 1835. Two other Mexican states did the same and many other areas of Mexico had insurrections. The newly formed Texas army defeated Santa Anna's army and Texas declared itself a nation in 1836. While US citizens individually joined in the conflict for many reasons, the US government did not offer any support. In 1845 Texas voted to join the US as a state, the only US state to have been an independent country. The major reasons for Texans wanting to join the US would have been the military support of the US and the US assumption of the national debt.

Mexico did not recognize Texas as a country, and there were some small battles, but Texas remained independent between 1836 - 1845. Upon joining the US the issue was forced and the result was a war between the US and Mexico which ended with the US accepting the territory between Texas and the Pacific Ocean in a forced settlement.

This is such a big subject I find it tough to come up with book suggestions. A good place to start is Duel of Eagles by Jeff Long, it focuses on the Alamo. I have not yet read Big Wonderful Thing: A History of Texas by Stephen Harrington but I have many other things he has written and enjoyed them.

For the average US settler moving to Texas in 1834 I believe the expectation that they would one day be part of the US was fairly low. For a US settler moving to Texas in 1844, the expectation would have been fairly high.