Hagana is Tzahal, or Tzva Hagana Leumi. On the eve of independence, the Etzel, or Irgun Tzva Leumi, and “Stern Gang,” more properly known as Lehi for Lohamei Herut Yisrael, merged into Tzahal and formed one organization. Originally, Etzel was Tzahal, but broke away from it because Yaakov Meridor and company perceived the British as the enemy, especially after the sinking of the Struma. But they didn’t become a truly effective fighting force against the British until 1944, when Menahem Begin assumed the leadership. Lehi became known as the “Stern Gang” because of its leader, Moshe Stern, a very daring, swashbuckly sort of guy, who was eventually captured by the British unarmed, and killed in captivity, causing the infuriated Sternists to become the most fanatically militant of the three. They were the ones responsible for the assassination of Lord Moynh (sp?). In addition to fighting Arabs or British, all three organizations were also involved with smuggling in Jewish refugees from Europe, running the British blockade and providing false identities to the ma’pilim.
Correction:
You stated: Hagana is Tzahal, or Tzva Hagana Leumi
As far as I know Hagana was Hagana. It was the predecessor of The IDF (Israel Defense Forces or the acronym ZH”L)
Tzahal stands for Tzva Hahagana L’Yisrael
The rest of your statement seems right on.