ZBW Controller reported frequency charting error on a third party chart; and also confusion with the Jeppesen charts for BTV airport.

Narrative

Working 52/53 with light traffic. Aircraft X checked on 2300 heading 190. I did not have a data block on Aircraft X. Scanning my EDST Aircraft list; I observed an active flight plan on Aircraft X off of BTV. I also observed a Mode C target with a correlated beacon just off BTV on a 190 heading which I concluded was Aircraft X. Knowing that the aircraft was well below my MIA and unsure of any obstructions in the area (I do not have any obstructions depicted on my video map within 30 NM of BTV; despite there being mountains nearby) I instructed the aircraft to contact BTV Approach on 121.1 and that I would talk to them in a minute. I noticed in their reply that they were communicating on 120.35.A few minutes later BTV Approach performed a radar handoff on Aircraft X. I accepted the handoff as normal; and a few moments later Aircraft X checked back on; on frequency 135.7. I said something to the effect of 'welcome back' when they did so; and they replied.A few minutes later; once the traffic had calmed down; I queried Aircraft X as to where they had gotten the frequency. They said it was on their chart. I asked Aircraft X if BTV Tower had specified which frequency to contact and they said no. I told Aircraft X that I had seen this problem before and was collecting information for a safety report. I told Aircraft X that other pilots had reported to me that the Jeppesen chart was confusing. Aircraft X said their chart was not Jeppesen but a European chart. The FAA charts only have 121.1 on them. 120.35 is the frequency to use at night when BTV Approach is closed; and works on the ground at BTV. It appears both frequencies are listed on Jeppesen charts as well as whichever company's charts Aircraft X uses.I asked the Aircraft X crew to fill out a safety report after they landed; and told them I would do the same. I said I would like to get the chart clarified so we don't have this issue in the future. I know I have [reported] this issue in the past; and I know other Controllers in the area have experienced it.The third-party charts need to be edited to clarify that 120.35 is departure frequency when BTV Approach is closed; and 121.1 is the departure frequency when BTV Approach is open.BTV clearance delivery should specify the departure frequency (121.1) until the charts are corrected; and it would be good practice to always specify it. BTV Tower should specify the departure frequency rather than saying 'Contact departure' until the charts are corrected.