The posted link (
http://maplesandbox.ca/2012/renunciation-and-relinquishment-what-are-the-differences-is-there-a-difference/ [nofollow] ) is useful but there is no practical effect between relinquishment and renunciation except this: the USG is not obliged to acknowledge your loss of citizenship except by formal act before a consular officer. That may be the only way to obtain a CLN and (as Boris Johnson found out) you may be denied boarding on an aircraft to the USA without one.
BUT the real distinction in this matter is the date of loss of nationality. Post 2008 loss -- especially for "covered expatriates" -- can subject you to draconian tax consequences, and that can include non-US family-member joint assets, PFIC (typically ISA, some pre-current tax treaty pension assets, investment assets, trust funds, and so on). One should avoid OVDP if at all possible.
Those who lost US citizenship pre 1967 (Afroyim case) or pre 1980 (Terrazas) will not have had it restored UNLESS they "availed themselves of an attribute of American citizenship" (as to taxes, see Rev. Rul. 75-357, PLR 8138071) -- and seeking a CLN can be just that. (The reason is that no state can attribute its nationality to a person without his consent or that of his parent/guardian except at birth, adoption or (sometimes) marriage.)
It is true that there's an international-law rule that every state, and only that state, determines who are its nationals. But the UK Supreme Court seems to be deciding for itself who are nationals of foreign states, most recently in the expatriation of extremist Islamists. The US Treasury has sought to include mutual collection provisions in new tax treaties but they do not apply to citizens of the other country (who were such citizens when the tax was incurred). State is seeking to include provisions for extradition of those accused of tax crimes (without a condition of "double criminality"). Very occasionally as in the Barrett case "ne exeat republica" writs have been used to keep tax debtors from leaving the US after a visit:
http://www.irs.gov/irm/part5/irm_05-021-003.html [nofollow] The TECS network can enable the IRS to monitor the travel of noncompliant taxpayers
http://www.irs.gov/irm/part5/irm_05-001-018r-cont01.html [nofollow] There are between 3.5 and 7 million expatriate Americans (nobody really knows how many; most probably do not have US passports). Only a few hundred thousand US tax returns are filed from abroad. You do the math.
The above points to a conundrum for those claiming to have lost US citizenship but who have no CLN (and choose not seek one) and who want to visit the USA. Best advice: travel via Canada. Unless the TECS system contains contrary data the traveler may be admitted and if the point needs to be litigated Canada is close. Hey, Plattsburgh Airport advertises itself as "Montreal's USA airport".
