This would never happen. There is no historical example of a helot being made a Spartan citizen. It would run counter to all the principles of Spartan society; it would be considered legally, politically and morally unthinkable.

All the citizen bodies of the Ancient Greek world were highly exclusive. Citizenship was determined by birth and citizens kept their rights and privileges to themselves. Your parentage determined where you were a citizen; some states considered any child of a single one of their citizens to be a citizen, but others (including Athens and Sparta) required both parents to be citizens. It was usually impossible to become a citizen of any Greek state except by formal decree of the governing body (usually a council or assembly). No single citizen would have the authority to make such a decision.

Indeed, since Spartans were particularly jealous of their status and closed to outsiders, it would have been even harder to become a Spartan citizen than to join the community of any other Greek state. We know of some individuals and a few groups that were made Athenian citizens, but there are only a few rare cases of single people being honoured with Spartan citizenship. These people would never be unfree to begin with.

But this brings me to your other question. The difference between "Spartan" and "Spartiate" is that the former can be used to indicate any free inhabitant of the Lakedaimonian state, but the latter is used to indicate only the fully enfranchised Spartan citizens. All Spartiates were Spartans/Lakedaimonians, but not all Spartans/Lakedaimonians were Spartiates. We tend to confuse these terms in modern usage, but the ancient sources are usually consistent about their use. They will usually indicate a group of people from Sparta and its territory (say, an army) as "the Lakedaimonians" (often translated "Spartans," a term which the ancients rarely if ever used), but when they refer only to full citizens who went through the upbringing, wear the cloak, and so on, they may use the word "Spartiates". For example, Herodotos specifies that the Spartan army at Plataiai consisted of 35,000 helots, 5,000 freeborn Lakedaimonian perioikoi, and 5,000 Spartiates.

This means that while it would be impossible for a helot to become a Spartiate, they may technically become a "Spartan". In the course of the Classical period, many helots were granted their freedom - usually in return for military service, but also for other reasons. A fragment of a lost work on the Messenian Wars claims that there were many words for these manumitted helots: aphetai ("the released"), adespotai ("the masterless") and other more ambiguous terms. But the vast majority, including the helots who served under Spartan commanders like Brasidas and Agesilaos, were known as neodamodeis ("new members of the people"). These were often settled in border areas to form new semi-independent communities of free non-citizens. They were Lakedaimonians, but not Spartiates.

By the time of Sparta's fall from power in the middle of the fourth century BC, there were many thousands of neodamodeis and their descendants. Some of these may have been able to send their children to Sparta to go through the Spartiate upbringing, and to live alongside Spartiate children; they might even come close to Spartiate status if they had the right connections (which largely meant submitting to pederastic relationships with prominent Spartiates). But even their distant descendants would never become full citizens unless a reorganisation such as that of Agis and Kleomenes in the late third century BC included them in the new franchise.