This is an answer about terminology in general. (As always, I'm answering as a learner who has thought about the learning process rather than as a tescher, but I hope it will be relevant.)
I think that in order to learn the true meaning of a term, one must first understand the concept that it refers to. Ideally in that order: if possible, encounter the concept first and then learn the name for it. (This is the same as when learning a foreign language.) Then when you do learn the name—probably immediately after learning the concept—you're not misled by the common meaning of the word. You already know the meaning: what you didn't know was the word for it.
For example, I think I was taught about limits not long after getting used to the idea of asymptotes in the context of curve sketching. First we were shown some examples of sequences and sums like
$$S_n=1+\frac12+\frac14+. . .+\frac{1}{2^n}$$
We spent a bit of time playing with these and learning how to express the sums in shorthand using the $\Sigma$ sign
For the above example, it was easy to see that increasing $n$ made $S_n$ get closer and closer to $2$ without ever quite reaching it. And once we'd understood that, we were ready to be told something like
$2$ is called the limit of the sequence as $n$ tends to infinity and we write it as $$\lim_{n\rightarrow \infty }S_n =2$$
At this point there was nothing confusing about the word limit because we were already familiar with what it was describing. Tends to seemed a slightly odd phrase, but was just an instance of mathematics sometimes using funny language.
The same went for the notation: we weren't introduced to a strange new symbol followed by a definition to grapple with and misunderstand—we were introduced to something needing the symbol, then to the symbol itself.
Summary: I don't think terms which differ from their ordinary usage have to be confusing, provided they're not the first thing we encounter. After you've seen what the limit of a series is, the most obvious English word for it is limit, so it's not a problem being asked to use that word. The problem arises if we try to get the concept from its name, rather than the other way round.