There are said to be two major extremes of Cthulhu gaming/storytelling, with a "purist" approach at one end, derived from a notion of what Lovecraft's philosophy implies about the investigators' unimportance in the larger universe, and the "pulp" approach at the other end, derived from a supposedly "looser" interpretation evolved from the more optimistic and active heroic action-adventure pulp magazines and comic books at the other.
The broad category described here as "Pulp" refers to stories, scenarios, etc. that fall towards the Pulp end of this Purist-Pulp scale. The investigators are likely to physically fight monsters with fist and gun, engage in car chases and globe-hopping adventures, dynamite Great Old Ones and topple idols. They have relatively high chances of coming out on top (for now). "Pulp" tends to emphasize action and adventure over atmosphere of wonder and dread, and in some cases (such as the BRP rules set) the term might imply both greater danger in the scenarios themselves, and optional "beefed-up" investigators - called "heroes" in BRP Pulp Cthulhu - with extra hit-points and special abilities that render them tough enough to withstand the adventure, and representing roles that might not commonly be associated with traditional Lovecraftian stories (soldiers, adventure-archaeologists, gangsters, hard-boiled detectives, mad scientists, etc.); scenarios intended for use with those rules may be extremely deadly when used for standard investigators. Players more familiar with more traditional horror and science fiction stories by Lovecraft, with more typical Lovecraftian characters (dreamers, poets, antiquarians, artists, etc.), may find the pulp setting somewhat disconcerting until they are used to it, due to its heavier emphasis on adventurous characters diving into the thick of danger and expecting to come out alive. In many cases, the "pulp" setting is moved from the default "Jazz Age" of the 1920s, up to the 1930s and even 1940s, and the mythos threats tend to be a little larger-than-life in scope, including fascist government cults of personality, international criminal masterminds, super-villains, wars between mythos factions, and the like.
In contrast, "Purist" scenarios tend to be set in 1920s "Lovecraft" country (or, more rarely, modern small-towns assumed to be customizable to resemble your town), where the scenarios tend to pit more subtle mythos threats against characters meant to resemble ordinary people.
Note that Lovecraft, though many of his stories are the model for what is thought of as "purist" stories, has written in both modes, or rather across the spectrum of the two modes, and that the "purist" should not be taken to imply that Lovecraft wrote purely in a "purist" mode.
Generally speaking, a pulp mode of gaming probably best favors longer campaigns, while an extremely "purist" mode typically tends to favor one-shot scenarios.
As an RPG Setting
BRP/CoC Pulp Cthulhu
-In BRP rules, note that the rules for Pulp Cthulhu: Two-Fisted Action and Adventure Against the Mythos (AKA Pulp Cthulhu) generally greatly expand the hit points, luck, and special abilities of Pulp Investigators (called "Heroes" in Pulp Cthulhu), and scenarios intended for use with those rules may be extremely deadly when used for standard investigators. The "Pulp Cthulhu" rules are actually little more than a set of optional, add-on rules that a keeper can pick-and-choose from in deciding how much or how little "pulp" to add to the rules, with the difference in scenario writing largely being one of writing style and the amount of emphasis there is on combat and such.
Note that long before the Pulp Cthulhu rules were published, there was a "pulp" side to BRP Call of Cthulhu, with some scenarios, consciously or not, tending to be more "pulpy" in tone - with investigators traveling the world to face deadly international Mythos conspiracies and the like, and can be thought of as the forerunners of modern Pulp Cthulhu.
D20 Cthulhu Pulp
The D20 Call of Cthulhu rules can by default imply a certain amount of "pulp" quality, with options to expand hit points and points available for stat point-buy and other distribution schemes, as well as the D20 rules for "leveling up" an adventurer (not required, but a default option in the more famous D20 settings), and the cross-over rules for D20 (3rd/3.5/Pathfinder) Dungeons & Dragons all have a similar, and likely even more extreme, effect to the BRP Pulp Cthulhu rules for "pulpier" characters. The writing style and 1930s setting used for some (though not all) of the published D20 adventures - specifically "Lost Temple of Yig", are very "pulpy" in their inspiration and effect.
"D20 Cthulhu" scenarios seemed to depend on who wrote them for whether they fell on the pulp/purist ends of the spectrum, with little formal attention to marking a philosophical difference: the modern scenarios in the rule book seemed to generally fall on the purist side of the spectrum with a cinematic feel to them, while other writers wrote 1930s scenarios specifically with pulp rules in mind.
Trail of Cthulhu Pulp
"Trail of Cthulhu will support both Pulp (for Indiana Jones, Robert E. Howard, thrilling locations sorts of games) and Purist (for intellectual horror and cosmic dread)." In Trail of Cthulhu, certain skills are capped at given levels for a Purist scenario, and unrestricted in Pulp, with a similar effect to the mechanical allowances of Pulp Cthulhu and D20 Call of Cthulhu.
Trail of Cthulhu seems to divide its scenarios into "purist" and "pulp" categories, depending on which side the scenarios were written for, and assumes a choice between one or the other modes (or a parallel set of scenario rules designed for a choice between the two modes), rather than an adjustable continuum between them, and offers advice for keepers in how to run scenarios and other content for one option or the other.