I don't see the difference between "последний" and "прошлый". For both words, I find definitions like "last", "past", "latest", and "recent". Are they interchangeable, or is there a difference?
They aren't interchangeable in most cases, as they correspond to different meanings of "last".
"Прошлый" is a simple word. Its primary (probably sole?) meaning is "the one that happened in the past, before the reported/implied moment". The time span may vary according to the context, but time is the key. This word is strictly temporal — it can't be used in any sense other than time. For example, you can't say "прошлый" about the last chapter in a book or the last dollar in your pocket.
- "прошлый втроник" = "last Tuesday" — the Tuesday that was immediately before the reported moment.
- "один из прошлых вторников" = "one of the past Tuesdays" — some unspecified Tuesday from the recent past, not too long ago.
- "прошлый опыт" = "past experience" spanning one's entire previous life, in the general context of life.
- "прошлый опыт" = "the previous experiment", in the context of chemistry class.
- "прошлые заслуги" = "past merits" — depending on the context, that sense of "past" may denote a nuance of "no longer relevant to the current state of affairs/events", "obsolete".
"Последний" is by far more versatile. It can mean "the previous one", and it's the only sense in which these two words are interchangeable:
- "На последнем уроке мы начали изучать причастия" = "На прошлом уроке мы начали изучать причастия" = "In the last (previous) lesson we started studying participles".
But "последний" has other meanings that don't coincide with "прошлый", and in which case they're not interchangeable.
- "последняя версия" = the most recent version (model) of something.
- "прошлая версия" = the previous version, the one before the latest version. Depending on the context, it can also refer to any of the older versions as well.
The last one, the final one in the context of time:
"последний этап" = "the last stage", in the context of some industrial process.
"прошлый этап" = "the previous stage".
"бар работает до последнего посетителя" = "the bar is open until the last visitor leaves".
*"бар работает до прошлого посетителя" makes no sense.
"последний вторник" - sounds weird if taken out of context. As if time stopped and there'll be no more Tuesdays.
"последний вторник июня" = "the last Tuesday in June" - this one is fine.
"прошлый вторник" = "last Tuesday", relative to the reported moment.
*"прошлый вторник июня" hardly makes any sense.
The last one is in a context other than time, in which "прошлый" would make absolutely no sense because its meaning is strictly time-related:
- "последний в очереди" = the last person in line", the person at the end of a queue.
- "последний этаж" = the last floor, the topmost floor in a building.
- "последняя конфета в коробке" = the last piece of candy in a box.
"Последний" can also mean "the latter" and "of the lowest rank", but these meanings seem to be beyond the scope of this question.
Последний means "last", прошлый means "past".
They're just about as interchangeable as English "last" and "past" are: in some cases they are, in others they're not.
Последний год means "last year", meaning a year after which there is no year like this anymore. It can be in the future. 2024 год — последний, в котором будет выпущен Шевроле "Камаро" means "2024 will be the last year the Chevrolet Camaro will be produced".
Прошлый год means "the past year". It's always the year before the current one (within a narrative's frame of reference).
The noun прошлое, which is a nominalized neuter adjective, means "the past".
One thing that is different between English and Russian is that прошлый rather than последний is used for set calendar intervals like минута, час, день, год etc. in the relative meaning. "Last year" (meaning the calendar year before the current one) would be прошлый год (modulo case).
For "last visit, episode, lesson" and pretty much anything else that is not a calendar interval, in the sense of "the prior one closest to now", both последний and прошлый are ok. "Past visits, episodes, lessons" in the sense of "the ones before now, not necessarily the last" would be прошлые, like in English.
In the majority of cases, "последний" means "last/latest", "прошлый/предыдущий" means "previous".
"Последний" works with the order in a queue, while "прошлый" emphasizes past time.
They're sometimes interchangeable:
"Прошлый месяц" (cannot be ongoing!) = "Последний месяц" (worse) = "latest month" = "previous month".
...and sometimes not:
"Последний гладиатор" = "the last gladiator" ≠ "Предыдущий гладиатор".
След - an effective mark of anything. След - a footstep mark on the ground, a wet circle of the water drop, a line of exhaust gases on the sky causes by plane.
Последний - it is a final/finite of something, if something have a chain of similar effective marks - a sequence of steps. So, mostly последний = last("track, footprint, footstep, trace") or seldom latest - он прибежал последним / he came running last.
Прошлый is literally "gone"("шл" от шёл/идти - went/to go), something that gone, not about directly time/time period like past, but, probably, something that gone by time, it can be the time - time period, it can be a thing that belong to you in the gone times. About the car (that I sold) I can say мой последний автомобиль - the lastest I had, but, probably I still have it, because I don't point out a finit of what I mean, maybe last that I bought, or мой прошлый автомобиль - the car that I had but it was gone, here is no variants, I don't have it.
Современные словари говорят, что "прошлый" от "прошлое"(past time), однако, если мы посмотрим этимологический словарь Даля, то там прошлый/прошлое от прохаживать (to go/to walk).
День проходил, а ничего не сделал; только попусту проходил. - (here is two variants of sense word "проходил", because "to go" can be about a day - time period, and about that I had passed through(there) all day) The day was ending, and I didn't do anything; I just wasted my time. / or / I wandered all day, but I didn't invent nothing usefull; I have not filled my existence with any sense - my wandering was senseless. - here is time~the way of life, that is why wandering
Старое добро прошло, а нового не видать. - literally old good had gone, and no sight of new one.
Если посмотрим картуслов, то увидим предпочтительные ассоциации переводов слова прошлое: last, go, passed, come, get, walk и только потом years, time, кроме того way, old. Советую ориентироваться на этот ресурс, так как он является контекстным и русскоязычным - переводит русские слова на английский, а не наоборот.
If you will translate forms of the word прошлое like past you can get this confusions:
Not "all time passed fine"))
Слово последний картаслов переводит как: last, lately, final, recently, last thing, last few, last time, end, years, only.