First, your Android x86 machine would not use OTG for this, nor would your Android phone. The Android-x86 machine is a host, the phone is the device. OTG is to make your phone into a host, so you can attach a "device", such as USB Mass Storage. You can then copy or move files between devices using a number of means.
Second, the two most common ways to do this are MTP and USB Mass Storage. These two methods are otherwise completely unrelated. One has nothing to do with the other. USB Mass Storage exports the device file system to the host as a raw device, like a hard drive partition. The host must have file system drivers. Because the host accesses the raw device beneath the file system, you can not allow the device to access the file system at the same time. You'll find the SD Card unmounted when the host attaches and you often can't mount "internal storage". MTP works more like FTP. Complete files are transferred from one device to another using a service on the device. This means the device can use file systems that the host doesn't know about and the two can share filesystems.
Due to pressure from Microsoft and limitations of the FAT filesystem, Google is moving away from USB Storage.
There are other ways to transfer files as well, such as using USB or Wifi networking and a host file sharing protocol such as FTP. Personally, I like the web-based add-on to FX File Manager. This gives a relatively complete file manager you can access with a standard web browser. I also have MTP working on my Linux devices, but on my Remix host, I just use FX or one of the many other built-in network tools (sshfs, samba, etc).