That's generally what it means, where "wedding" is essentially "a ceremonial event where you invite friends/family/loved ones to observe and celebrate the new marriage." You do still have to show up in person though (so there's opportunity for a picture); basically you can still get married without ever having what most people would define as a wedding.
Like, my dad and his wife didn't have a wedding; they got married at the courthouse on a Friday morning and then took little weekend vacation together to celebrate, just the 2 of them. They still had someone snap their photo in front of the courthouse, but nobody came with them or anything; it was just the two of them and the court staff.