I came to like it means like at first you may not have liked it but then you started to like it more and more over time. I got to like it means that you had an opportunity to like it in the past, although it doesn't sound very proper to me lol, hope this helpssssss :).

herpderp614 messages are right.trust ur instinct

"I came to like it" is more like 好きになった or 気に入るようになった. "I got to like it" is a bit strange, but it could mean 好きじゃなくてはいかない or 気に入らないと駄目. "You gotta love it!" is something you might hear. It means that you can't help but love it. 気に入らない事は無理

They mean the same. you can say "I got to like it over time". but like the previous commenter said, we usually don't say "I got to like it", it sounds strange. "I got to ___" also can have other meanings, and they are much more common. for example "I got to try a new kind of food when I visited japan".