At the most general level TEMA addresses features that are partiucular to shell & tube heat exchangers that Code does not. Some examples are baffle thickness and clearance to the shell, tie rod standards, instrument connections and many others. Design of the actual pressue boundary is usually governed by Code.
Code generally is mandated by law in various jurisdiction, TEMA standards are not.
If you are talking about tubesheet design, Part UHX is much more detailed that TEMA. It more "accurately" accounts for elastic properties in the perforated and unperforated regions of the tubesheeet, and of the tubes. It takes into account stresses in cylinders integral to the tubesheet.
Part UHX calculations require that nearly all details of the design are known to perform tubeshet design. TEMA standards solve for a thickness directly, Part UHX solves for stresses and therefore is usually an iterative calculation. TEMA calculations for other than fixed tubesheet exchangers can usually be solved with pencil and paper in a few minutes. I am not sure Part UHX calculations can be solved by hand at all.
Still, fabrication and testing are mostly governed by other parts of the Code such as Parts UG, UCS, etc.
Part UHX is mandatory under the Code, TEMA is not.
No doubt I've left out some important differences...
