Open a TCP socket directly to one another. REAL Studio has good classes to make a socket connection, either for listening (server) or initiating (client). Nearly every language has such libraries either built-in or available.
You then pass any series of octets you want. This is totally flexible, but you have the burden of figuring out your own protocols for packaging and shipping data back and forth. This process of exchanging data is known as marshaling or serialization.
This approach works even if both apps are running on the same machine. Two local apps can make a socket connection even without a network. Simply use the internet/host address "127.0.0.1", or domain name "localhost", both of which means "this computer".
Either app can act as a web server (an HTTP server), returning plain text rather than HTML in response to certain URLs requested by the other app. Super simple & easy approach for getting single or few pieces of data.
Instead of a web browser making the HTTP request, the app uses a socket or HTTP-client library to make the HTTP request.
Two good books on HTTP include these from O'Reilly.
HTTP Pocket Reference
HTTP: The Definitive Guide
Remember: HTTP <> HTML
HTTP is the usual way we deliver HTML, but the two are not bound together. You can make requests and responses over HTTP that have nothing to do with HTML and web pages. Likewise, you can deliver HTML content without HTTP, such as "rich text" email messages.
…returns a single line of plain text rather than a bunch of HTML making up a web page:
• Web Service
Either app may be able to act as a Web Service server, while the other makes a SOAP, REST, or XML-RPC call. XML-RPC is the simpler and saner predecessor to SOAP, as described well in this this book.
Or both apps can read and write data via a 3rd server's services.
This idea is similar to the bullet above, "HTTP", but formalizes how to make requests with arguments, and how to represent data.
One app writes a file in a location to be read by the other app.
Either app reads or writes data to a database server such as Postgres.
You can even handle requests and responses this way. Create a table of 'requests' or 'to_do_items', where either app creates a row in that table to ask for work to be done, and the other app is in a loop scanning for such rows being inserted.
• Message Queue
Both apps can use a 3rd party message queue service.
You can even use email for this, where each app gets their own email account on your email system so they can send and receive messages on their own.