I will argue with the comments here, and say that these two sentences do not say the same thing, from a developer's standpoint.
I helped my colleague with the algorithm.
This indicates that your work impacted the algorithm itself -- perhaps you wrote a mathematical proof for it, gathered some research which led to its creation, pulled some all-nighters with said colleague to refine it, or so forth.
I helped my colleague with the implementation of the algorithm.
The key here is that the implementation of something is not the same as the creation of the object itself. Saying you helped with the implementation of the algorithm implies that it was fully formed by the time your work commenced, and that you only helped with a practical application, such as programming it into some piece of software or translating it to a specific programming language.
From your the beginning of your question, the latter appears to be the case. If this is some well-known, proven algorithm, then saying you helped with it is vague and obviously not entirely true. If it's a lesser known algorithm, that may be construed as downright plagiarism. The point is, the implementation is something you and your colleague created, whereas the algorithm likely already wholly existed beforehand.
Edit, to match yours:
Ah, now that you've clarified, I understand what you're asking. Technically yes, the two statements are of the same form -- the reason why the two are interpreted differently is the default action of the objects. What does a brush do? It paints. That's pretty much it, barring more minor applications. Now look at an algorithm: when you think of its default use, I imagine almost no one jumps straight to helps people. Algorithms do a lot of things, but helping people isn't the default (and it would be indirect, anyhow). Because an algorithm is something that is created and manipulated by a person, it makes more sense in the original context to assume you meant that you were helping someone do something to the algorithm, not vice versa.
How can this be made more clear? Supplement using for with, as with is vague:
"Helped my colleague using the algorithm."
"I painted it using a brush."
Ambiguity is your enemy in official reports. Clarity is key here, especially if your superiors are more likely to skim the report than slowly comb through it.