Several types of printed circuit boards are used for TI cartridges. In RPK and ZIP style cartridge images, they are referenced by their type name.
Standard
This type is used for most classic cartridges.

Cartridges may have 0 to 5 GROMs; their contents have to be dumped contiguously from the first GROM to the last. If the dump file is less than 40 KiB long, the remaining locations in the GROM space are filled with 00.
The cartridge may contain ROM, which must be dumped as one contiguous file. Here as well, remaining locations are filled with 00.
Original TI cartridges always have at least one GROM and possibly a ROM. Third-party cartridges were usually built without GROMs, but these cartridges are locked out in later consoles like in the TI-99/QI. This was in fact an attempt of Texas Instruments to block third-party cartridge development.
Write operations to the GROM and ROM spaces are ignored.
Extended Basic style (paged)
This format is used mainly for Extended Basic. Later formats took this format as a base.

Similar to the standard format, there may be 0 to 5 GROMs. In this case, there are two ROM banks that are selected by a write operation into the ROM space. This leaves the contents unchanged, but switches the banks. The written value is arbitrary.
In fact, the actual ROMs in the Extended Basic cartridge are organized in a different way: There is one 4 KiB ROM that occupies the range from 6000 to 6FFF, and an 8 KiB ROM consisting of two 4 KiB banks that are visible in the area from 7000 to 7FFF. The write operation just switches the banks in this second area.
In ZIP cartridges, this PCB type is named paged12k. In RPK cartridges, the paged type should be used. The first bank is mounted in the rom_socket, while the second bank is mounted in the rom2_socket.
Mini Memory (minimem)
The Mini Memory cartridge contains one GROM and a 4 KiB ROM. The second half of the ROM space is used by NVRAM.

The NVRAM is buffered by a battery in the cartridge. In MAME, the NVRAM contents are stored in a file in the nvram path and loaded on the next run.
The full GROM space is available, but the only cartridge to use this type is Mini Memory with a single GROM.
Super Space II (super)
The Super Space II cartridge is an Editor/Assembler cartridge with additional buffered RAM of 32 KiB capacity. The RAM is visible as four banks of 8 KiB each, which are mapped into the ROM space by setting a CRU bit.

The base address is 0800, so the bits to be set are 1, 3, 5, and 7 (yielding twice the offset, so 0802, 0806 etc.).
One way to select a bank is to make sure that no other bank is currently selected, then use the SBO (set bit to one) instruction:
LI R12,>0800
SBO 1
This turns on bank 0. However, it is recommended to use the LDCR instruction which sets or clears multiple CRU bits in a row so that it is ensured that only one bank is actually selected.
LI R12,>0800
LI R1,>0080 // 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 = Bank 3
LDCR R1,0 // 0 means 16
If there is a valid ROM header at the memory address 6000, the name in the header will be shown in the cartridge selection list.
MBX cartridges (mbx)
Cartridges from MB (Milton Bradley) may have a special PCB type inside, which is called "MBX".
The GROM space may be populated by 0 to 5 GROMs as with other PCB types. The ROM space, however, is a bit unique:
There is a ROM of up to 16 KiB size, which is mapped into the space from 7000 to 7FFF as one of 4 banks of 4 KiB each. The bank is selected by writing the bank number into address 6FFE. In the space from 6000 to 6FFF, bank 0 is always visible. Also, there may be 1 KiB of buffered RAM located at 6C00 to 6FFF, shadowing the ROM.

Note that MBX cartridges may rely on additional hardware that is not (yet) available in the MAME emulation. That is, the cartridge may be correctly set up, but fails to start because the hardware is not detected.
Paged7 (paged7)
This is a rare format, used by TI CALC, maybe by others as well. It is similar to the MBX scheme, but without the RAM. Also, the banks are switched by writing any value to 7000, 7002, 7004, or 7006.
The ROM may take up to 16 KiB, available as one of 4 banks of 4 KiB each, and bank 0 is always visible at 6000 to 6FFF.

Paging by CRU (pagedcru)
Cartridges with this type of PCB make use of CRU bits to select one of 8 banks (total of 64 KiB). In fact, they work like the Super Space II cartridge, but without a GROM.

Paging by 74LS379 (paged379i)
The 74LS379 circuit contains 4 flipflops, so 16 different combinations may be used for activating a bank of 8 KiB. Since the outputs are interpreted as active low, setting 1111 means bank 0, 1110 is bank 1, and so on until 0000 which is bank 15. The bits are taken from the address where the write operation is done (0110 0000 000x xxx0).
That is, the contents of the ROM are reversely selected by the address bits, which is why this type is called "inverted" 379i.

The maximum capacity of this cartridge is thus 16 x 8 KiB = 128 KiB.
Paging by 74LS378 (paged378)
The 74LS378 circuit contains 6 flipflops, so 64 different combinations may be used for activating a bank of 8 KiB. The bits are taken from the address where the write operation is done (0110 0000 0xxx xxx0) and are directly used as the bank address.

The maximum capacity of this cartridge is thus 64 x 8 KiB = 512 KiB.
Dump files for this cartridge are usually named like xxxx_8.bin which indicates the paged378 scheme in other emulators. In MAME, the name is not used for determining the type but the PCB type entry in layout.xml.
Cartridges of this type are also known as the UberGROM cartridge. However, unlike the UberGROM, the paged378 type does not support GROMs (yet). If GROMs shall be included, the gromemu type must be used instead.
Paging by 74LS377 (paged377)
The 74LS377 circuit contains 8 flipflops, so 256 different combinations may be used for activating a bank of 8 KiB. The bits are taken from the address where the write operation is done (0110 000x xxxx xxx0) and are directly used as the bank address.

The maximum capacity of this cartridge is thus 256 x 8 KiB = 2048 KiB = 2 MiB.
GROM emulation (gromemu)
Cartridges of this type make use of a GROM emulation: Instead of proper GROM circuits they store the contents in an EPROM or FlashROM and use a special circuit that manages the autoincrementing address typical of GROMs. However, the circuit does not deliver the current address in the GROM space; this is handled by the console GROMs instead.
Since a normal EPROM is used, there is no limitation of 6 KiB per 8 KiB slot. The whole range of addresses in the GROM space may be used.
For the ROM space, the gromemu type offers two modes: In the normal mode, 12 address bits are used to derive the bank number, so 4096 banks are possible (with 8 KiB each). The bits are takes from the address where the byte is written to: 011x xxxx xxxx xxx0.
In the paged mode, it behaves like an Extended Basic cartridge, but then only two banks are supported. The mode depends on the presence of a ROM2 dump. In there is none, the normal mode is assumed.

The bank bits in the address are automatically activated by the dump size. That is, for a 16 KiB dump (two banks), only a single bit is used: 011x xxxx xxxx xX0, the others are ignored. For a 32 KiB dump, two bits are used: 011x xxxx xxxx XX0, and so on.