Тhe difference is that lately has more of a continuous or repetitive meaning - продолженное или повторяющееся значение - similar to the perfect aspect/tense - and doesn't work well for individual events,
while recently can be used for both.
I went to the library recently and
I've been going to the library a lot recently are also both fine.
I haven't seen her lately and
I haven't seen her recently are both fine.
* problem - trouble - concern - issue. разница
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