The root meaning of Torah is "instruction", and of Talmud is "learning". It could be said that meaning of Torah is Instruction (though most people translate it "the Law", and the meaning of Talmud is "the Learning" so that doesn't say much. You have to know how it is used. In Judaism the Torah is identified with the 5 books of Moses, and the other two sections or groupings are the Prophets (Nevi'im) and the Writings (Ketuvim). Put them first letter of these three together, and vowels and you get the Bible (the Christian Old Testament) TaNaKh. The Torah section of the Tanakh is also called the Torah shebekhtav - the Torah that is written (because it is is in written form). This is to distinguish it from the Torah she-be-al-pe (the Torah that is "on the mouth"), that is, the Torah that was not written but passed from mouth to mouth,
From Moses, to Joshua, to others - the prophets, to "men of the great assembly, to the "pairs", among whom are Hillel, and Shammai, etc. It was believed by the Pharasees that with the written Torah, there had to to be an oral Torah that was passed down in order to know how to interpret the written.
For instance, the Torah that is written says not to work on the Sabbath. But it doesn't define what work is. How to apply it? Well the Oral law, the Torah she-be-al-pe defines it for each generation. So there are "twin founts" for instruction. After many generations, the Torah she be al pe was itself written down, but though it was understood to come from God as an explanation to what He had Moses write in the written Torah, the rabbis tried to keep the written Torah prime, so they called the other torah, now written down, "Secondary". The word for secondary is Mishna.
So this is first part of what is called the Talmud. Or you can say that theTalmud is made up of two parts - the Mishna and something else. The Mishna is in 6 main sections or "Orders", and is mainly in the Hebrew language, being produced mainly in the Hebrew speaking areas of Israel, and in its later recognizable form appears to be a more "people's" common spoken Hebrew. So this dialect of Hebrew is often called Mishnaic Hebrew. Modern Hebrew is more a development from Mishnaic Hebrew, rather than Classical (Biblical) Hebrew. The Mishna was composed by many teachers, rabbis from 200 BC to 200 AD. But just as the Mishna was a sort of extension and commentary of the Torah, so the Mishna itself was commented on. This latter commentary - like the Mishna containing both precise commandments (Halakhah) and stories, parables, reminiscences, (Aggadah) - was composed over 300 years, from 200 AD to 500 AD, mainly in what had become the strong center for the Jewish people, as they were now persecuted by the Romans and then the Byzantines in Israel (Palestine). This strong center was Babylonia, and since Aramaic was the prevalent language in Babylonia, the second work of commentary, and that being a commentary of the Mishna, was written in the Aramaic language. Since it was understood to be a completion to the Mishna, it was called the "completion" or "the finishing". In Aramaic the word is Gemara. And it is the Mishna and the Gemara together which came to be known as the "the Talmud" (the Learning) Though the term Talmud is understood to be the Mishna and the Gemara together, some Jews refer to ony the second part, the Gemara, as the Talmud. But all understand what is involved.