The differences between TI LM4040/LM4041 and LM4040-N/LM4041-N

The “-N” suffix in Texas Instruments parts such as LM4040-N and LM4041-N series signifies that the parts are originated from National Semiconductor before Texas Instruments purchased National Semi.
LM4040/LM4041 are TI designed devices that were created before the acquisition.

LM4040-N/LM4041-N and LM4040/LM4041 have similar specs but have different options.
For example, LM4040-N/LM4041-N parts have AEC Q100 automotive grade option where the LM4040/LM4041 from TI do not.
Also LM4040-N/LM4041-N has more accuracy and temperature range options

There is no difference between the two series.

Each series LM4040-N/LM4041-N and LM4040/LM4041 has its own data sheet.

The part numbering structure for LM4040-N/LM4041-N and LM4040/LM4041 is different too.

Part numbering structure for LM4040-N/LM4041-N:

Part numbering structure for LM4040/LM4041:

LM4040-N/LM4041-N parts are more popular, but, as per TI, both part will be kept in production.