TE (Terse Executable) is a simplified version of PE defined in some of the UEFI specs. To quote [0]:
> The Terse Executable (TE) image format was created as a mechanism to reduce the overhead of the PE/COFF headers in PE32/PE32+ images, resulting in a corresponding reduction of image sizes for executables running in the PI Architecture environment. Reducing image size provides an opportunity for use of a smaller system flash part.
> TE images, both drivers and applications, are created as PE32 (or PE32+) executables. PE32 is a generic executable image format that is intended to support multiple target systems, processors, and operating systems. As a result, the headers in the image contain information that is not necessarily applicable to all target systems. In an effort to reduce image size, a new executable image header (TE) was created that includes only those fields from the PE/COFF headers required for execution under the PI Architecture. Since this header contains the information required for execution of the image, it can replace the PE/COFF headers from the original image. This specification defines the TE header, the fields in the header, and how they are used in the PI Architecture’s execution environment.
Given it is a modified version of PE, I think it still counts as a member of the PE family of executable formats. It isn't something with a different heritage, such as ELF. Although ELF and PE are ultimately cousins – AT&T invented COFF, and then they invented ELF as a successor to COFF to fix its flaws; other vendors, such as IBM, SGI and DEC, decided to extend COFF to remedy those flaws instead of adopting ELF; and then Microsoft took AT&T COFF and made their own modifications to it to produce PE.
> The Terse Executable (TE) image format was created as a mechanism to reduce the overhead of the PE/COFF headers in PE32/PE32+ images, resulting in a corresponding reduction of image sizes for executables running in the PI Architecture environment. Reducing image size provides an opportunity for use of a smaller system flash part.
> TE images, both drivers and applications, are created as PE32 (or PE32+) executables. PE32 is a generic executable image format that is intended to support multiple target systems, processors, and operating systems. As a result, the headers in the image contain information that is not necessarily applicable to all target systems. In an effort to reduce image size, a new executable image header (TE) was created that includes only those fields from the PE/COFF headers required for execution under the PI Architecture. Since this header contains the information required for execution of the image, it can replace the PE/COFF headers from the original image. This specification defines the TE header, the fields in the header, and how they are used in the PI Architecture’s execution environment.
Given it is a modified version of PE, I think it still counts as a member of the PE family of executable formats. It isn't something with a different heritage, such as ELF. Although ELF and PE are ultimately cousins – AT&T invented COFF, and then they invented ELF as a successor to COFF to fix its flaws; other vendors, such as IBM, SGI and DEC, decided to extend COFF to remedy those flaws instead of adopting ELF; and then Microsoft took AT&T COFF and made their own modifications to it to produce PE.
[0] https://uefi.org/sites/default/files/resources/PI_Spec_1_7_A... PDF page 269