LTC2325-16 Channel to channel matching

Full-scale error is defined as worst-case deviation of the first and last code transitions from ideal and includes the effect of offset error. This is essentially a gain error, not a TUE.

Typical curves on page 11 of the data sheet show Full-scale and zero-scale matching over temperature. Typical curves on page 9 of the data sheet show INL and DNL matching. The channel numbers are not shown. 

Thanks for the response.  A gain error is an error that scales with the input.  So if an input changes 2x or 4x the corresponding voltage error( due to gain error) also changes 2x or 4x etc.. The inclusion of the offset error in the full scale error seems to me to be more like a total unadjusted error, as it would include both offset errors and gain errors. 

This is how ADI defines gain error. You will see that it is very similar to the LTC2358 definition of full-scale error.

Gain Error The first transition (from 100 ... 00 to 100 ... 01) occurs at a level ½ LSB above nominal negative full scale (−4.999981 V for the ±5 V range). The last transition (from 011 … 10 to 011 … 11) occurs for an analog voltage 1½ LSB below the nominal full scale (+4.999943 V for the ±5 V range). The gain error is the deviation of the difference between the actual level of the last transition and the actual level of the first transition from the difference between the ideal levels.

Thanks again for trying to help here. I agree that description your listing is essentially the same for full scale error and gain error. However I would argue that is not a typical definition of a gain error. The gain error as I have seen the term used, is an error that scales with the input.

The link below (from Analog's website, in their "glossary of EE terms") defines gain error as I would expect. They refer to the slope of the line on a graph between input and reported output, which is the behavior I'm trying to describe when I say it scales with the input.

I don't think the full scale error here is the same thing because it includes the offset error.  I could assume that the offset error (zero-scale error) is constant across the input range, and assume that the difference between that value and the full scale error scales linearly with input voltage, that would meet the terms of what I'm calling a gain error,  But I'm not sure that's a valid assumption.  I'm also not sure if it's safe to assume the calculated gain error would be identical across multiple channels.  The full scale error graph I mentioned before seems to indicate that it's not.  

https://ez.analog.com/data_converters/precision_adcs/f/q-a/574426/ltc2325-16-channel-to-channel-matching/507748

Gain Error
What is Gain Error?
Definition
The gain error of a data converter indicates how well the slope of an actual transfer function matches the slope of the ideal transfer function.

Gain error is usually expressed in LSB or as a percent of full-scale range. Gain error can be calibrated out with hardware or in software. Gain error is the full-scale error minus the offset error.

I believe both definitions are saying the same thing in a different way.