양력 (also 태양력) is the normal, official solar calendar that everyone uses the world over including Korea.
음력 (also 태음력) is the lunar calendar which was official in Korea until 1895. Nowadays this calendar is only used in connection with traditional holidays such as the Lunar New Year (음력 설) and Chuseok (추석, Full Moon Festival - 음력 8월 15일). I believe there are very few people left now who remember dates by this calendar.
We now use 양력 pretty much for everything. Some people used to keep track of birthdays in both calendars in the old days (until mid to late 20th century), but I doubt any ordinary people do these days.
I'm prettry sure you won't have any trouble at all even if you don't know anything about 음력. It is a thing of the past which might appear in old movies and storybooks.