If we set autgrowth for log file as restricted then logs size will increase up to specified limit and then it will start discarding old logs and new logs will be there in logs.
This is wrong. If it has to grow it will grow until the max size and after which further growth request will result in failure. You are confusing things with log truncation, which is the process which allow log physical file to be reused (so it doesn't have to grow). I have an article explaining how log grows and what is the role of truncation in this, see How to Shrink SLQSQL Server log.