Memory Stick & SD card Storage Limits

I'm trying to get educated here. For example, when I try to export say 300 photo files from my MAC's Photos App. to a 2 GB flash drive, you are telling me that about 100 files get transferred to and fill the root which causes messages that say no more files can be transferred because the root is filled. These 100 files consist of roughly 140 - 150 MB in my case. So now, the root is filled but there is about 1850 MB still available in the drive. Why don't the remaining 200 files get transferred to the free space or why don't the 300 files get transferred to the free space initially?

In your first message, you asked if I was exporting to the root. I didn't know I had a choice of where in the memory stick I could export to. Is there a way to direct the export to the larger free space of the drive and avoid the limited root space, besides the two-step process directing them to a Desktop folder and then dragging the folder to the stick icon?

So, are you saying because I use a FAT format, I can only export about 100 files to the stick even though it has a much greater capacity and the only way to get around that is to use the folder technique?

Your suggestion worked both for the USB Stick and the SD card. Thank you so much. It makes you wonder how it happens that the exported items go to the drive root, and is there a way to avoid that.