NLX, LPX, and Mini-LPX
NLX LPX Mini LPX
LPX form factor has no expansion slots but one slot in the middle of the board that allows it to host a bus riser card.The NLX has the same thing, however the expansion slot is at the end of the board. Also the NLX is standardized, unlike the LPX.
LPX or mini LPX uses a riser card ( also called a bus riser or daughter card). LPX motherboard has the riser card near the center, whereas the NLX motherboard has the riser at the edge of the board.
There are no similar form factors to ATX if you're talking about a slimline. Slimline form factors are NLX and LPX. The form factors to ATX are BTX, Micro-ATX, and Flex-ATX. There is no correlation between slimline and ATX.
NLX has slots parallel to the motherboard as ATX does not
NLX
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NLX BTX ATX
The NLX form factor has a riser card on the edge of the motherboard.
ATX, MicroATX, Flex ATX, BTX, and NLX, In that order.
NLX has expansion slots parallel to the board to allow smaller cases but may limit the number of expansion slots, rather than perpendicular like the ATX