The EMSE portion is just the suffix that defines the package style, temperature grade, lead-free option, etc for the part. In this case, the first E in the 'EMSE' suffix defines the temperature rating of the part, where E is for Extended temperature range (-40 to +85C). They also offer parts with a (C)omercial, (I)ndustrial, (H)igh Temp, (M)ilitary, etc ratings. The next three letters are the package code for the part where 'MSE' indicates the MSOP package with Exposed GND paddle. According to the datasheet for the part, it's also available in a 16pin DFN package which would have a 'DHC' suffix. So you will need to determine if you want the 16-pin MSOP package (MSE), or the 16-pin DFN package (DHC). The pinouts are the same, but the footprints are different. The DFN package is physically smaller than the MSOP option if size is a concern, but you may want to factor in part availability and cost as well.
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Here is a PDF from Linear's site that breaks down the suffix information in more detail if necessary.