This is a simple question with a complex answer - sorry for the lengthy reply.
Please note that there is a difference between Phonak RemoteMic and Roger Clip-on Mic, which is explained further below.
The short answer to your question is: the difference between Roger Pen, Phonak RemoteMic and Roger Clip-on Mic is the microphone pick-up patterns.
- the Roger Pen has 3 different microphone patterns depending on the orientation of the pen. See pages 23, 24 & 25 of the Phonak User Guide or the table at the end of this post for details. The Roger Pen also has Bluetooth capability to connect with a smartphone.
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- Do not confuse the Roger pen with the Roger Easy Pen which does NOT have bluetooth capability nor manual microphone control.
- The Roger Clip-on Mic has a single, focused microphone pattern that is the same as the Roger Pen in Lanyard mode. The other major difference is that the Roger Pen can connect via Bluetooth to a cell phone, and the Roger Clip-on Mic does not have bluetooth capability.
- The Phonak RemoteMic has an omni-directional microphone pattern, and uses a bluetooth connection rather than the Roger FM Receiver.
The Phonak RemoteMic uses a bluetooth connection to a ComPilot or other bluetooth receiver connected to hearing aids, and has a non-focused (omni-directional) microphone pick-up pattern. I find this useless in noisy environments like a restaurant because it just amplifies everything. I ended up using it only to set in front of a TV so that I didn’t have to turn the volume up too loud. This cannot be ‘paired’ with additional microphones, so cannot be used to create a multi-talker network array.
The Roger Clip-on Mic can connect to a Roger Receiver and/or be used as part of a microphone array or multi-talker network by connecting to a Roger Pen, Table Mic or other Clip-on Mics. The Clip-on Mic has a similar focused microphone pattern as the Roger Pen in lanyard mode. A very focused pick-up pattern which is better for noisy environments if you are trying to hear one person. The Clip-on mic should be no more than 20cm/8in from the speaker’s mouth. So in use, when I’m having dinner with someone, they clip the Clip-on Mic to their shirt/blouse and I can hear them very well. If having dinner with several people, I use the Roger Pen as the primary device and create a microphone array, some people wear the Roger Pen, others wear Clip-on Mics, and I can hear whomever talks first, until they stop and the next person starts talking. It’s not perfect, but much better (for me) than not using multiple microphones.
If you’re not tired of reading yet, see this link for even more details of the Roger system and uses. Scroll past the pictures of hearing aids to the What is Roger? section for a general explanation and a diagram of Roger Pen’s 3 microphone patterns.
Scroll to the Compatibility between Microphones section for explanations of multi-talker networks.
Roger Pen Microphone pick-up patterns. (Figure 11 from this link)