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Я сумею о себе позаботиться. --- {суметь}
Но нет ничего такого, с чем мы не смогли бы справиться, да? --- {смочь}
It seems that both "суметь + infinitive" and "смочь + infinitive" means "be able to do something" or "manage to do something", but I wonder if they are simply interchangeable in the two sentences above? Or do they carry nuances?
By and large they're interchangeable.
One slight difference they may have is in that я сумею implies ability exercised in spite of any obstacles or adverse circumstances, it has a resilience undertone.
я смогу just indicates general ability without going into any further specifics as to the mode of exercising it.
to be able and to manage as possible translations for both verbs, but the truth is in daily speech я смогу + inf often means я сумею + inf, being a kind of its simplified version, their distinction isn't consistently maintained
Jan 17, 2018 at 21:27
In my opinion, the primary difference is not about 'resiliance VS general ability' but rather between суметь as 'repeating actions' (iterative) VS смочь as momentary action.
Most of Russian prefixes usually make a perfective form, which can be iterative or momentary.
Semantically, суметь comes from уметь - 'to know how to' - and смочь goes back to мочь (may &/or can); therefore it's possible to say
Я смогу дойти.
Я смогу ходить.
Я смогу гулять.
Я смогу погулять.
Я смогу прогуляться.
but not (or possible just under some specific circumstances)
Я сумею дойти.
Я сумею ходить.
Я сумею гулять.
Я сумею погулять.
Я сумею пpогуляться.
The reason is that verbs like жить, ходить, играть, дышать or гулять and most of their prefixised forms have habitual connotations, which don't quite get along well with iterative infinitive.
я смогу прийти вовремя VS я сумею прийти вовремя, the second phrase already implies possibility of some obstacles the speaker might need or is going to overcome in order to be on time
Jan 17, 2018 at 12:22
я смогу ходить, there is an implied снова, so, like after an injury he toughs up to be able to walk again after rehabilitation. In я сумею дойти there is some kind of uniqueness of circumstances, "I will be able to walk this route at -50 and in heavy snow, because I need to fetch a doctor", but not that one has tried this before in a similar setting, although one definitely can walk in general. Hope this helps.
Jan 17, 2018 at 20:49