A wetlab doesn't refer to any specific set of equipment. It refers to all the stuff that you do that involves transferring liquids between test tubes via pipets, heating and cooling them, etc., in contrast to "dry lab", which refers to computational data anlaysis. Depending on the type of sample, the wetlab preparation will vary. For example, if you have an extremely small amount of starting material (e.g. you want to sequence the DNA of individual cells), the prep will be different, or if you want to sequence RNA from blood, you need a step to remove all the mRNA that encodes hemoglobin, which is 50-75% of the total mRNA.

I do dry lab exclusively, so I'm not sure what the most bsaic sample prep procedure consists of, and whether the equipment needed for that prep can be made portable. But in the field, you're going to have to contend with contamination issues, since tiny amounts of contaminating DNA can mess things up big time. I don't think you can just carry around a portable autoclave, so maybe the solution would be individually-wrapped sterile prep kits, maybe with the possibility to sterilize, reset, and re-wrap them back at home.

It might be possible to do the preparation steps with portable gear. "Classic" DNA extraction with multiple rounds of electrophoresis or PCR aren't strictly necessary for all applications.

Still, it would be easier to carry the sample back with you rather than carry the equipment into the djungle.

On the other hand a lab in a developing country might have less trouble using the MinION rather than sending away the samples for sequencing.

A wet lab is a lab as you might imagine it on CSI, i.e. the whole nine yards.

Sometimes, components of this can be miniaturized to create a "lab on a chip", but that takes another level of technological development.