Why don't you just use the official terms weak and strong atheist to avoid confusion?
Assuming this is rhetorical, but I will go ahead and answer anyway.
Weak atheist and strong atheists, defined by some (certainly not officially), are two sub categories of atheism. Weak atheism has two varieties implicit and explicit. Strong atheism is only explicit.
Of weak atheism we have implicit, which adds nothing to atheism, and is essentially a meaningless category which includes everything in the universe (including the universe) and every mental construct that is not capable of forming belief. This group has no position. This category is completely superfluous. So, I do not, personally, refer to such as atheist.
Next we have the weak explicit atheist. Weak explicit atheists reject the proposition that God exists, and reject the proposition that God does not exist. These are considered by some to be atheists because they do not believe God exists. But a further analysis of this group yields that this groups position is that God exists is equally likely as God not existing. Another grouping can also be described by people who believe God exists and that god does not exist. The only differences between these two groupings (weak, explicit atheists and this other grouping) are 1) one accepts both propositions while the other rejects both, and 2) what looks for evidence to exclude while the other looks for evidence to include one of the propositions. Thus, the difference between these as far as I can see, rests in semantics.
The last category of atheism is strong atheism. This group actually believes that God does not exist. While the level of conviction may vary, this group is saying something very distinct.
So we have a total of three position and one non position, but a total of 5 categories.
1) theist- those who believe the proposition God exists is true, and the proposition that God does not exist is false. Position: God exists.
2) unnamed- those who accept both propositions (God exists and God does not exist). Position: that gods existence is equally likely as God non existence.
3) weak implicit atheist-anything incapable of acceptance or rejection of either proposition. Position: n/a
4) weak explicit atheist- those who reject both propositions (God exists and God does not exist). Position: that gods existence is equally likely as God non existence.
5) strong atheist- those who believe the proposition God does not exist is true, and the proposition that God does exist is false. Position: God does not exist.
As you can see, 1 and 5 are equally different from the other categories. Category 2 is the same position as category 4, and the inclusion of this position into a category that is the same as 1 or 5 is semantics at best. And category 3 isn't even a position so it's inclusion cannot add anything to whatever category it is included. If it cannot add anything, then its deletion doesn't subtract anything.
Language is designed to communicate. We should strive for efficient communication. Categorizing 2-4 with either 1 or 5 does not reach this goal. Categories are generally made by common characteristics, the common characteristic that people who wish to group 3-5 choose to focus on is "not believing God exists." This is justified by the fact that atheism is is defined by these people as not theism. That 2 is also not theism but still has a belief in God is seldom discussed.
However, in all of this, there is another camp. Those who assert that atheism is just #5 and theism is #1. This group, while not putting every conceivable thing into a box, is internally consistent in their logic.
So, why don't I use the terms strong atheist and weak atheist? Simple, because I like internal consistency.