The Musimathics books are great to understand frequency and its filtering. While Vol. 1 explains in one chapter what frequency is (as well as how and why), Vol. 2 offers a whole chapter on frequency filtering. You can pretty much leave the equations out in case you’re not interested in math and the explanations are still amazing.
After reading it, it feels like when Neo starts seeing bits and bites everywhere around. Still, musically I didn’t get rid of all the Agent Smiths yet though 
I’ve recently been wondering how filtering works on a, like, mathematical/electrical level, thanks for mentioning this book, looking forward to checking it out…
EQ’s are filters. There are a lot of filters, a 4 pole ladder being one of them and a bandaxall EQ being another. All of them are mixing positive and negative phases of various filter functions (and possibly feedback) together.
I don’t think you are missing anything. They both boost or cut frequencies and there isn’t a commonly used term for “thing that boosts or cuts frequencies” that includes both eqs and filters.
I think the issue of color is separate as either thing can be implemented in a totally clean or very colored way.
Either one can be used creatively during songwriting/sound design or surgically during mixing/mastering but filters usually the former and eq usually the latter.
The main difference is the curves. Make sure not to confuse shelving eqs with low/high pass filters. Different curves different resulting sound.
But so many EQs are loved for how they color the sound! 
I personally think of EQs and filters as one and the same, to be honest. I mean, there are different filter designs in the digital and analog domains, like diode filters, ladder filters, chebyshev, biquad, butterworth, etc. But at the end of the day they’re pretty much doing the same thing.
(Edit: grammar)
It would be fun to do an A/B test and oscilloscope comparison test between various EQ tests and filter comparison. I may do this in my feature as I love to tinker and tweak with stuff.
There is no inherent difference. They’re both filters. If you compare any specific filter to any specific eq you will find differences but comparing two specific eqs (or 2 different filters) will yield similar results. In the most basic sense they are the same thing.
They do similar things, but filters are usually low pass, high pass or band pass, and can vary in intensity from one to the next. A 12db low pass filter is not as steep as a 24db low pass. EQ’s on the other hand can offer more options, such as shelf, tilt, bell, etc, also varying in steepness of curve from one to the next. Filters often have a resonance setting, which boosts the peak, but some EQ’s have something similar for certain bands called a gain setting.
For me, generally, I use filters on synthesizers, samplers, or standalone to shape a sound and impart a character into it. I usually use EQ’s during the mixing and mastering stage, or if something just isn’t sitting right.
And yes, filters are more fun. I would want to party with a filter, but I would want an EQ to do my taxes.
Likewise the PE-1 eq from ALM is also a nice character EQ, you can drive it quite nicely and it definitely adds a bit to a digital source. It is supposed to mimic the EQs on a portastudio.
Then there are things like scientific filters which are specifically meant more for analysis and isolation than character.
It might not be commonly used, but I’m pretty sure it’s accurate to say they both filter the sound. I suspect an electrical or electronic engineer would not argue with that.
Has anyone tried modulating the EQ like a filter?
EDIT: Looks like I can only modulate the Low Gain/High Gain on the Hydrasynth, still an interesting effect.
The DJ style EQ on the OT is v nice sounding and I oftentimes modulate it.
It’s a great alternative for filter modulation.
That DJ EQ is fun, and kinda dirty (in a good way)!
I’m also a fan of modulating the frequency and Q of the non-DJ EQ on the OT with a full cut in the mids – basically a notch filter. I like using p-locks and slide trigs for that
Yeah they are both great and different sounding enough for creative use.
With samples that are pitched down a lot it’s great to have EQ’s that allow bringing back some presence as well.
The DJ EQ has a nice character to it for sure.
I wonder why it doesn’t have adjustable freq though.
Isn’t it fair to say, that a filter always filters, whereas an EQ can, but might not necessarily and only boosts frequencies instead?
There are so many kind of filters, like dual peak self-oscillating resonant stuff etc, so likely not.
People also use highpass filters all the time for boosting low-end for example.
What I mean is, that even if a filter is boosting, it is technically still filtering. Otherwise it would be an EQ as I understand, because an EQ might boost only (without filtering).
This is what google offered:
gerund or present participle: filtering
pass (a liquid, gas, light, or sound) through a device to remove unwanted material.
I can’t think of any example off the top of my head, other than resonant and/or distorting audio filters and IG style photo filters where filtering would include adding or boosting something and even then I’d say that with those two examples the term filter is a bit misused.
Enhancer might be a better term.
I have no idea though hehehe.
I think we’re at the limits of the accuracy of the language. By the strict definition of a filter being something that only takes something away a resonant filter that can self-resonate breaks that definition even more than an EQ by generating sound all on its own! 
I agree. I just didn’t write that a filter only filters, but always does