1. “学会了” is a fixed phrase to express "sb has got to learn sth". "会了" means you not only tried to learn it and really gained the knowledge or skilled taught. For example, "我学会了这些词" means I learned these words and now I can remember them, understand them and use them properly. You can also say “看会了” or "听会了", if you want to emphasize the way you learned it is observing or listening only. For example, 我没看乐谱就听会了这首歌. 2. "v+完了" means finished/completed. For example, “我学完了这些词” means I've finished studying all these words. "我看完了一本书" means I've finished reading a whole book. 3. "了" itself is a quite flexible and subtle auxiliary word, it is usually used after the verb to indicate that the action has already happened. “学了” doesn't have to mean "学会了", otherwise all students will get full mark on what they learned.

简单说， “学了”不等于“学完了”，“学完了”不等于“学会了”。 学会了>学完了>学了， 程度上递减。 补充一下，“学会了”并不一定代表“学完了”，严谨一点就说“全部学会了”，同理的就不赘述了。

會means abilities or capabilities, 學會 means you have learnt and acquired some kinds of skills. the 3 sentences above are very similar. 學會了 emphasize more on acquiring the skill. you have leart those words and know how to use them. 學完emphasize you have just finish the learning process. 學了 just means you learnt something. in above situation, we usually use 學了，學會了is also ok. we seldom use 學完 in such case. after we completed a course, we can say 我們讀完了一個課程

学了和学完了是一样的，了有表完成的作用。但学会了有点不同。学了不一定就会，但学会了就是掌握了。