You're welcome. If I called Nashua Approach, it was a mistake, it should be Boston Approach. Let me know if you can find the timestamp where you're hearing "nashua approach".
Boston Approach provides Class C service within the Outer Area (a 20nm radius) of the Manchester airport (b.eyond the published Class C airspace) That's why the rectangles reference that distance. As to why they don't show any on the west side, I'm not sure, I don't know/care about the layout of that airspace

When you're IFR, those details cease to matter. In fact, it wouldn't have mattered if I was VFR either because I was handed from Boston Center to Boston Approach during the descent in any case, so I would've also ended up on the appropriate frequency. Interestingly, though, the NY Sectional chart does show 3 freqs for the Manchester Class C (bottom left of the chart, the airfields are listed alphabetically), even though the map only depicts two freqs.