MySQL - Like with index
Exactly. Which is why some databases use alternative indexing mechanisms for text. SQL Server has a full text indexing capability that works by breaking the string into WORDS, removing bad ones (like "in" in english - happens too often) and then uses a different syntax for finding words in the text index.

Standard SQL Indices are simply not suited for the task.

MySQL, from a 30 second run in google, also seems to have a full text search mechanism.