(Func, Action, Predicate) VS Converter and Comparison delegate c#

Now I'm confused in Converter and Comparison delegate,why .Net Framework introduced these 2 delegate flavours for just converting and comparing, when and how to use these 2 over existing 3.

Historically, the delegates were introduced in the opposite order to the order your question suggests.

Predicate<T>, Converter<TInput, TOutput> and Comparison<T> were introduced in .NET 2.0. They were used by List<T> and a few other types. At this point in time C# didn't support lambda expressions but did support anonymous methods. Delegates were mostly used for event handling and starting threads... supporting them for predicates, conversion and comparison was a baby step, effectively.

Note that Predicate<T> isn't used for comparisons - it's used for testing a single value. For example, you could have a Predicate<string> for "Is the string length more than 5 characters?" Comparison<T>, however, is for comparing values - it's used for sorting.

The Func and Action delegates were (mostly - Action<T> was in .NET 2.0; used by List<T>.ForEach) introduced in .NET 3.5, with LINQ. That was the time frame in which C# 3 introduced lambda expressions and its LINQ support as well, and suddenly delegates were everywhere. I believe the level of awareness of delegates (and how they could be used) went up massively with C# 3.

Early pre-releases of LINQ used Predicate<T> instead of Func<T, bool>, but then additional overloads of Where were introduced accepting Func<T, int, bool> to allow the index to be part of the predicate.

I suspect that if the framework were redesigned from scratch, the "special purpose" delegates (Predicate<T>, Converter<TInput, TOutput> and Comparison<T>) might not exist. It's possible that Predicate<T> and Comparison<T> would still exist, as they provide additional semantic hints as to the purpose of the delegate which can help readability - but Converter<TInput, TOutput> really doesn't have any benefits over Func<T, TResult>.