Is it possible to connect the Ethernet port (of a Raspberry Pi) directly to a Modbus TCP RJ45 port (such that the devices can talk to each other)? Or is this not possible without a converter?
I am unsure if this is the correct forum, but I believe this should not be specific to the Raspberry pi.
Short answer - Yes... But....
As per the comments this is possible but there are a few things you will need to do (i.e. some configuration will be needed).
I think it's worth nothing that "Modbus TCP RJ45 port" is not really a meaningful term. Modbus is an application layer protocol; this depends upon a number of underlying layers:
You don't need to understand this in detail; the point is that before ModbusTCP will work you need to have a working TCP network (which all Modbus-TCP devices will support; generally via an RJ45 Ethernet connection). As such a better question probably is "If I run a CAT-5 cable between a Raspberry Pi and another device (Modbus TCP unit) will I be able to connect via TCP?" (a lot more people know about TCP/IP networking than Modbus!).
The first thing to consider is Ethernet. Running a cable directly between two older devices will often not work because they needed a crossover cable. Almost all modern equipment (including the Pi) supports Auto MDI-X which means the cable will just work. You can also connect the units via a switch (and doing this removes the need for Auto MDI-X).
Next you need to consider the IP layer. When you connect your Pi to your home network it will (usually!) be given an IP address by a DHCP service (usually running on your router). If you are connecting the Pi directly to the device then there will be no DHCP service so you will need to manually assign IP addresses to the devices (and ensure the subnet is correctly configured). A common way to check if an IP connection is working is to use the ping command.
With the lower layers working ModbusTCP will generally 'just work'. Many ModbusTCP devices also offer a browser based configuration and checking that you can access that is a good way to confirm that the network link is working.
One further question is probably "should I do this"; it's OK to hook things up this way to make some quick changes. However generally you will want the Pi to access other network resources so connecting everything to a router (home router will work; for remote devices a cell router is often used). You can either give the Modbus unit a static IP manually or use the routers configuration pages to assign it a static DHCP lease (otherwise it's IP might change from time to time).