I'll consider the low-pass filter as it is the most useful type in subtractive synthesis. A low-pass filter cuts high frequencies (HF) and allows low frequencies (LF) to pass unhindered. The user can set a cut-off frequency where the transition from LF to HF occurs.
In a standard DAW plug-in filter the slope of the filter is normally controllable and can be set to 6 dB/octave, 12 dB/octave, 18 dB/octave or 24 dB/octave. The greater the slope, the stronger the effect of the filter.
The cut-off frequency of a synth filter is similarly controllable. Since higher slopes are more useful in synthesis, sometimes the slope is set at a fixed high value.
So far so good. The two filters seem quite similar. So where are the differences?
Well firstly, a synth filter usually has a control for resonance. With this, a narrow band of frequencies just below the cut-off frequency can be boosted, often by a considerable amount. There isn't much need for this in a DAW, but in sound creation it can make a big difference. Oddly enough, the standard filter in Logic has a Q control that does the same thing. A high Q setting is illustrated above. In DAW operation this is most useful for a sound that doesn't change in pitch, such as a kick drum.
Perhaps the biggest difference between DAW filters and synth filters is that in a synth, the cut-off frequency changes as you play different notes. This is so that every note has subjectively the same sonic quality. Without this tracking, some notes are heavily filtered while others are hardly touched and remain 'buzzy'. There isn't a great deal of relevance for this in normal audio operation.
Although DAW filters and synth filters have similar jobs to do, they are adapted to their individual functions.
One thing that is worth trying however is to put an audio signal through a synth filter. There is considerable potential for creativity here and I strongly recommend trying it if you get the chance.