Hello Ben,
Generally any single box that contains at least a mic preamp, an equalizer, and a compressor is called a channel strip. Some strips also will have some kind of hard limiter, de-esser, or whatnot. They call them that because they are freestanding emulations of a single strip yanked up out of a mix console. Indeed, early channel strips were to some extent just that.
Now, there are many boxes that have only a preamp and eqalizer, such as the Neve 1073, which people do not call strips.
But then again, there is the Chandler TG Channel Strip which only has the preamp and EQ and yet is called a "strip" by the manufacturer.
So, the term can be quite variable, and the whole thing is rather semantic.
Some of the most important features I would consider in any channel strip are if each section can be used independently, if the EQ can be switched before or after the compressor, if the bypasses truely remove any given section from the signal path, and if the power supply is built into the unit (less desirable, imo) or separate (usually more desirable, but less portable).
Channel strips appear to have the advantage of shorter, hardwired signal paths, and so may reduce problems with cables that are wearing down, poorly maintained, and could arguably reduce RFI. Clearly a main advantage is size, weight, space, and they seem most useful for portable rigs.
Some people argue that the sound quality from strips is inferior to that of the same componants in stand-alone housing. While I think this may likely be true of the lower-budget type units, I would advise actual listening and be less hastey when considering higher end units.
The two channel strips I believe would be most attractive and reputable are the GML 2020 and Pendulum Quartet (I and II).
From a few listenings, I would personally feel that lesser boxes such as most the cheaper focusrites, and below, are not as desireable. But, I suppose one never knows till you try.
Hope that helps,
KT