“Ça, c’est […]” is equivalent to “C’est […]” as far as meaning is concerned.
“C’est […]” is just a contraction of “Ça, c’est” (in English it would be equivalent to “That’s“).
Roughly, you might say that in certain contexts there is no difference and both mean “That is” but that’s making abstraction of the finer points that may pertain to a particular context.
A/ Several contexts
1.– Ça c’est une banane, c’est ça? → That is a banana, right? [pointing]
In this case, « ça » is used because the child is either pointing at the fruit or holding it out to his/her mother’s gaze. In English, “that” will be stressed most often and this stressing justifies “ça” or vice versa.
In a more general case no pointing is necessary for the use of added “ça” to become meaningful; for instance, two persons talking about a certain subject come to a point in their conversation where one of the two has to give an explanation so as to rectify the other person’s misconception concerning a particular detail; at the end of the explanation the person that did the explaining might say “Ça c’est la raison.” in referring to the reason that has just been put forth in his/her explanation. The process, except for a detail, is just as in the case of the dialogue about naming fruits above: there is no physical pointing, but the pronoun “ça” stands for what is most obvious in the conversation, what’s most near in time, that is to say, the reason (or explanation); the possible difference is that in this case of “abstract pointing” “ça” can be done away with and the translation into English would not include sentence stress on “that” anymore.
2.– Dis maman, c’est quoi celui-là? → Tell me mummy, what’s that one called? (The child is pointing at another fruit.)
— (Ça) c’est un fruit de la passion. → That is a passion fruit. [reply to someone else’s pointing]
The mother is not doing any pointing but the addition of “ça” is made to connect to the pointing of the child and is pronounced with more force; however it is only an option, the mother can say plainly “C’est un fruit de la passion.”. In this case, “That” is not stressed and one can say that “ça c’est” and “c’est” are equivalent (and therefore have the same translation).
3.– C’est une orange? → Is this an orange?
— Non, pas celui-là. → No, this one is not. (No, not this one.)
— Et celui-là? → What about this one?
— Ça c’est une orange.→ That is. [contrastive assertion]
*In this context there is not often a deletion of “ça”, which is translated in English rather by “that” than by “that one”. Sentence stress in French will be on “ça” as it will be on “that” in English without fail. When in a rare case and to the same effect “C’est une orange.” is used instead, for the pronunciation to correspond to the context, sentence stress will have to be used on “c’est”.
In a non material context the process is the same.
B/ When there is not an antecedent clearly defined things are different : only « ce » can be used; as stipulated in the TLFi, « « Ce » is [then] the subject of a proposition with the fonction of attributing an identification ».
“C’est” is never the same thing as “ça c’est” in those cases.
C’est moi, toi, lui, elle; ce sont eux, elles; fam. c’est eux, elles.
C’est elle qui me l’a dit.
- C’est la course la plus longue de la journée.
- Ce sont les fleurs qui poussent le plus haut en altitude, ou tout au moins des fleurs de l’une de ces sortes-là.
When the above sentences are used (or more generally sentences of this type) one must be careful to make out whether or not there is an antecedent in the context (textual or “material”).
If you are at the door of your father’s house and you say “C’est moi, ouvrez la porte.” there is no “material antecedent”, you cannot use “Ça c’est moi, ouvrez la porte.”. If you are looking at school photographs with your girl friend and if, while looking at you, she points at your face in one of the photographs, you can answer “C’est moi.” or “Ça c’est moi.” as explained in “A“.
In the following sentences where “c’est” is used, it can never be replaced by “ça c’est”.
C’est le temps qui cause ces mauvaises récoltes. → The weather is responsible for those bad crops.
C’est le printemps! Allons nous promener dans la montagne! → Spring is here! Let’s go walking in the mountain!
C’est moi, ouvre la porte. → That’s me, open the door.