File transfer between two gsm modem
You cannot connect one GSM modem directly with another. GSM modems are controlled using "AT" commands, patterned after (but greatly extending) the AT commands developed in the original Hayes modems thirty years ago.

There is a core set of AT commands that are common across all cell modems; these generally have a prefix of "AT+". Then there are a number of proprietary AT commands developed by each cell modem manufacturer, they have prefixes like "AT$" or "AT%" etc where the third character is unique to the manufacturer.

I have worked with cell modems from four different manufacturers. The documentation for these commands typically runs over 500 pages long.

These are all designed to work only with a cell tower. There is a command to get the signal strength (AT+CSQ), which is used to update the bars on the screen. There are commands to check whether the GSM modem has registered on the network (connected to a cell tower). Another command to get the list of carriers supported by the cell tower.

For voice calls there is a command to dial a call (ADT, just like the dial up modems from the past), and another command (or rather set up of commands) to set up a data call and request a TCP/IP connection. When a call answers, or a connection is made to the Internet, the response is CONNECT. The modem then goes into a data where data can be sent or received. To get back to control mode, the familiar +++ sequence (patented by Hayes) is used.

If these were to work for point-to-point communication with another GSM modem, that other modem would have to have most of the capability of a cell tower. But there is no provision for that. There are no commands in any GSM modem AT set which allow a GSM modem to behave that way.

So you have a few options.  If your Arduino and PC are within 75-100 feet of each other, you should definitely look at using Bluetooth instead.  (The "official" range is 100m but that is for outdoors with no obstructions.)  This is by far the simpler method -- no data plans or host server to sign up for. 

You could upload your data to a server using your GSM modem on the Arduino, and download it from the same sever from the GSM modem you are attaching to your PC (which I assume you are connecting to using a USB to UART cable and virtual COM port).  In this case FTP would be a suggested protocol.  You should be able to get a host (server) which allows FTP access for $3 a month or so.  You will also need to get a SIM module for each of your modems and subscribe to a data plan just like a cell phone (not so cheap).

A less expensive option would be to forget about using the GSM modem on the PC and run your own FTP server exposed to the Internet from your PC.  This will require getting a fixed IP address.  Most Internet providers offer this option; I am paying $5 a month or so for mine.  (It is possible to run a server using a dynamic IP, but I think you would need to have DNS look-up capability on your Arduino -- I have written code for this, and it is not trivial.)

So in this case, the GSM modem on your Arduino would connect directly to the FTP sever on your PC.  You would only need to get one SIM card, and not have to set up a server.