Introducing yourself in Japanese

What is the difference between 'watashi wa Christel desu' to 'christel desu' if they have the same meaning 'I'm Christel'?

In simple terms, 「Watashi wa Christel desu」 is a little more formal, and 「Christel desu」 is a little more casual.

If you were to translate them literally,
「Watashi wa Christel desu」
is "I am Christel."
and
「Christel desu」
is just 「Am/is/are Christel."

While dropping the subject of a sentence often sounds strange in English, it's commonly done in Japanese, as long as the listener can understand what the subject is from context. So, for example, if Taro is at a party where a bunch of people are meeting each other for the first time, and various people in a conversation are introducing themselves, when it gets to his turn, he'd probably just say "Taro desu," since it's understood from context that everyone is giving their own name.

On the other hand, if Taro wants to speak more formally, or if he's not already in the middle of a conversation where everyone is introducing themselves, saying "Watashi wa Taro desu" is a little clearer and easier to understand.

Also, as a side note, it'd probably be more natural to use
「Watashi wa Christel to moshimasu」or 「Christel to moshimasu」
These literally translate to "I am called Christel," but the nuance is closer to the more natural "My name is Christel."

While 「Watashi wa Christel desu」/「Christel desu」are understandable, the nuance kind of comes off like "It's me, Christel," which could be a little confusing if you're talking to someone for the first time (i.e. it might make them think, "Wait, did I meet this person before/am I already supposed to know who they are?").

The difference is that the topic part (watasi ha), is often seen as being redundant in everyday Japanese. When you are introducing yourself it should be obvious that you are talking about [watasi] so "watasi ha" simply isn't necessary. You will learn more about when omission is and is not appropriate as you read and listen to more Japanese.