IME, growl is not an effect, it is innate to the instrument and its EQ setting/pickups/strings and it brought out by the player's technique. The fundamental is deemphasized by using a pickup near the bridge. There is, in effect, a mid boost in the just right band(s) to give a slightly speech-like quality to the instrument's tone.
A passive Jazz bass does it easily, as do Wawick thumbs (pickups near the bridge), and MM pickup equipped 'Rays, Laklands, and MTDs, to name but a few. IMHO, it is not over-driven, distorted, clanky, ganky, or zingy. It is a somewhat nasal tone color, perhaps even "horn-like."
Despite those qualifiers, I still love to cite Anthony Nembhart's little video from a few years ago. The sound is distorted and noisy due to the recording quality, but despite that, between times 0:10 and 0:18 you can hear real growl, not created by effects or overdrive, even though a bit fuzzy.
This example shows a great player on an inexpensive passive instrument strung with rounds. Note it has a single MM pickup.