I would argue that the latter is just a very specialized instance of the former. What is the cat picture with formulaic text if not a unit of cultural matter being shared and evolving?
We have random mutations: Socially awkward penguin[0] -> Socially awesome penguin[1]
Then there's sexual reproduction: Socially awkward penguin + socially awesome penguin -> socially awksome penguin[2]
The process of natural selection is popular appeal. There is certainly room for debate as to the cultural merit of popular internet memes, but I don't think there's a strong argument that they are not an instance of the concept as coined by Dawkins.
An excerpt from the intro Wikipedia entry on memes:
>an idea, behavior, or style that spreads from person to person within a culture".[2] A meme acts as a unit for carrying cultural ideas, symbols, or practices that can be transmitted from one mind to another through writing, speech, gestures, rituals, or other imitable phenomena with a mimicked theme. Supporters of the concept regard memes as cultural analogues to genes in that they self-replicate, mutate, and respond to selective pressures.[3]
We've had memes ever since we've had society.