We don't have separate words for earphones and headphones. Both are "наушники". But you can show type by using different verbs:
Я надел наушники.
Я снял наушинки.
Я вставил/воткнул наушники.
Я вынул наушники.
But the first pair of verbs can also be used for earphones.
In normal communication we don't make difference between headphones and the rest, but it may be shown by additional description. For example, earphones will be "наушники вкладыши", "вакуумные наушники" - vacume earphones. More spoken is "наушники затычки", but that's more like slang. Headphones will be just "большие наушники" or "закрытые" if they cover the whole ear. Also, Russians usually use word "headphones" in relation to any of them in English.