Dave,
ADSB and PilotAware P3i both show as moving aircraft on your screen - as per the ones on your screenshot. If you have the Pi Audio connected, this type give specific direction based alerts in the form 'Traffic, x o'clock, y Km, zz Ft Above or Below'.
Mode C or Mode S aircraft are known as 'Bearingless' targets, because we can't determine their location or 'bearing' from our own aircraft. This is determined by Radar units from the bearing of the radar head and the time taken for the transponder response to reach it. All PilotAware can do with this type of alert is advise on the presence of such an aircraft by showing a coloured warning 'ring' around your own aircraft, together with the relative altitude- which we DO know from its transponder transmission - displayed in or near the 12 o'clock position on the edge of the current 'ring' together with either the term 'Mode C' or in the case of a Mode S, the Aircraft Reg, which again we can obtain from the transponder. The colour (Green, Yellow or Red) and size of the ring helps denote the level of perceived risk, based on the strength of the signal your PAW is receiving from the other aircraft. This is regulated (modified) by the Mode CS Detect 'Range' filter you have selected in PAW 'Configure'. If you have the Pi Audio connected, this type of alert takes the form, 'Traffic Notice', Traffic Alert' or 'Traffic Danger' as the degree of perceived risk increases.
Until users get used to the form of Mode C/S alerts, it is easy to confuse the presence of a ring with either 'Mode C' or an 'Aircraft Reg' and the size of the ring as indicating the position or distance of the target, They DO NOT !! They are merely intended to prompt the direction of scan (i.e. above or below you) and advise on whether the risk is increasing due to the target getting closer. For this reason 'Bearingless Target Detection' is set to 'Off' in new units by default.
The fact that the pilot of G-CCZD said he had ADSB out would mean he should have shown up as a 'moving aircraft' long before getting that close to you, so it may in fact have been another aircraft altogether that triggered your first alert.
It would help us understand what was going on if you could post a screengrab of your PAW 'Configure' screen or confirm your present settings.
The 'normal' method for transferring large files such as Track Logs by the way is by using 'DropBox' and posting a link on here to the file, or PM'ing the link direct to Lee. If you don't know how to do this we can help you.
Best Regards
Peter