Texas doesn't have degrees of murder. Murder is murder. It can be classified as capital murder under circumstances where the death penalty is warranted.
Some article stated that it can be reduced to a 2nd degree felony in the sentencing phase if the jury decides there were mitigating circumstances.
So I guess instead of convicting someone of of “2nd degree” murder in Texas, you just convict them of murder, and then the defense has to make the argument that the facts of the case demand a lesser punishment during the sentencing.