This is a well discussed and easy to fix bug... Disconnect USB cable, go to Settings, Apps, and Show System Apps and find External Storage and Media Storage and clear data and cache on each one and reboot, then give it 5 min after full boot up to rebuild media databases and connect to USB and select MTP. Should be good to go.
EDIT: In some instances where the SD card contains a large number of (media) files, it can take more than 5 minutes for the databases to rebuild. There is no way to see if the status of this database buildup in the phone itself, so sometimes you just have to be patient.
Also note that some users have stated that this is not sufficient by itself, but sometimes the system cache partition needs to be wiped and rebuilt. Official instructions for performing this operation from Moto are here. Note that this operation can take significant time... 5-15 minutes, occasionally even longer, do not interrupt the operation.
Ok, this is a good fix...thanks. Although my problem was the other way round - my laptop could see the internal storage but not the sd card. I've been round and round tearing my hair out and this suggestion was the only one that actually worked for me - although slightly differently.
First off....I've got a Moto G 2nd gen recently updated to Marshmallow. Inserted a new 32gb sd to use as adoptable storage. Backed up my media ready to transfer over, but when I connected to my laptop via usb I couldn't see the new sd no matter what I tried. I could see the internal storage, but that was no use to me. Various "fixes" I found didn't solve the problem. Eventually I found sac1691's post above and tried it out as a last resort before going to bed. The only change I made was to "force stop" on "external storage" and "media storage". Then I connected my usb without any great hope of it having solved anything. Surprise surprise...it solved the problem. I can now see my new sd card on the laptop and transfer everything over that I wanted to.
I now can't see the internal storage via usb however. This seems to be a recognised issue (Google it) but that's not a major issue for me.
Many thanks to sac1691, and I hope that this helps anyone else who is suffering similar problems
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