"Gern/gerne" indeed means "gladly" or "happily" or "with pleasure" but it is often translated with "like" because Germans use "gern" to talk about things they like to do. In English, you say "I like to swim" (more common than "I swim gladly"), in German it would be "Ich schwimme gern" (more common than "Ich mag schwimmen").
"Gern" can't mean "compared to" or "similar to".
Ah, thanks. I'd misunderstood, as the first time or two I saw "gerne" in these lessons it appeared to match the "compared to/similar to" meaning of like.
Have to say this Adverb lesson is turning into a bit of a slog; three times in the last two days I've been at the very last or second to last part of a lesson and run out of hearts... sad owl is even sadder when it's the last damn exercise!