Engineering Practice Law
If the law is strictly interpreted, all engineering work is required to be stamped because the work consists of the practice of engineering as defined in the law. Read the law, as it is linked above, Section 1001.003. Practice of Engineering.
The law generally allows you to stamp only the work where you are in responsible charge and only for work in your particular discipline. For example, you can't stamp electrical work if you are a mechanical engineer.
However, there is no enforcement mechanism that ensures engineering work is stamped. So what happens is that a lot of engineering work is never stamped.
Engineering work that is submitted to the government for review or permit is stamped. That is because the government agency where the engineering work is submitted specifically requires the work to be stamped and the agency will verify stamping. Usually the particular agency lists the requirement that the work be stamped.
Under the Texas Engineering Practice Act, only duly licensed persons may legally perform, or offer to perform engineering services.
Don't understand why, but many engineers have some kind of libertarian mindset and seem to resent the requirement for licensing. If you are one of these, feel free to respond to the OP, but don't respond to me.