Yes modern weaponry is similar to some 40K weaponry and probably would still be useful but mostly against other humans that have similar weaponry.
Weaponry that we recognize today like shotguns, machine guns and other types of weapons still exist and are used in 30K/40K. They have the benefit of being relatively easy to produce without needing a lot of high tech knowledge, so low tech worlds in the Imperium are able to produce those themselves.
So no, they do not differ much in operation. However how powerful they are will differ a lot based on what materials used and the caliber of the gun.
Comparing a current day M4 with a Agripinaa pattern type II Autogun, which is described as having 8.25 as its caliber (which is significantly higher than the M4's 5.56), with its rate of fire and muzzle velocity not being impaired by the larger caliber with a rate of fire of 625 rpm and a muzzle velocity of 825 m/sec to the M4's 700–950 rpm and muzzle velocity of 910 m/sec.
So comparing two fairly common weapons of a similar type you can see: whilst very similar, the 40K rifle is more powerful due to its higher caliber. So I think it's safe to say that they are overall just stronger than current day rifles when compared. But I do think our weaponry could still be of use within some types of warfare in the 40K universe. Especially among other humans like in Hive cities.
As to how they are used and how effective auto rifles are.
Against other humans with similar level of tech they would still be useful. though they will be useless against anything among the line of Astartes or most Xenos races.
The technology, however, is also used by more advanced weaponry that is used by Astartes and Adeptus mechanicus.
Astartes terminators also use auto rifle technology in their Assault cannons which would be similar to how a modern day minigun would work.
It allows for more damage than similar caliber weapons due to its very high rate of fire.
However I think it's less about the workings of the weaponry but more about the ammunition that is used.
The technology of how Auto weapons are used is simple and effective and will work regardless of time period. What's more important is what type of ammunition is used.
Astartes Boltguns also work in a simple way just like auto weaponry, but are immensely powerful due to the power of the ammunition that is used. It is really big in size and detonates after impact, so they are basically mini rockets, but the weaponry that is used to fire them is pretty simple in inner workings.
Standard bolts comprise the following components: outer casing, propellant base, main charge, mass reactive detonator cap, depleted deuterium core, diamantine tip. The caliber of the standard round is .75 and it possesses a super-dense metallic core.
A sub-human race known as the Interex were encountered by the Luna Wolves during the great crusade. They were noted to heavily use Bows as a main part of their armament.
Horus Rising by Dan Abnett
The soldiers – variously gleves or sagittars, Loken learned – were almost as tall as the Astartes, but with their far more slender build and more closely fitted armour, they seemed slight compared to the Imperial giants. Abaddon, at the first meeting, muttered that he doubted their fancy armour would stand even a slap.
Their weapons caused more remarks. Most of the soldiers had swords sheathed across their backs. Some, the gleves, carried long-bladed metal spears with heavy ball counterweights on the base ends. The others, the sagittars, carried recurve bows wrought from some dark metal. The sagittars had sheaves of long, flightless darts laced to their right thighs.
Which the astartes were mocking them for:
‘Bows?’ Torgaddon whispered. ‘Really? They stun us with the power and scale of their vessels, then come aboard carrying bows?’
‘They’re probably ceremonial,’ Aximand murmured.
However at a later part in the book it shows them use the weaponry.
And it shows them to be superior weapons that easily best the Astartes Power armor used by the Luna Wolves
More flashes, like laser fire. Projectiles, moving so fast they were just lines of light, zipped down the colonnade, faster than Loken could track. Oltrentz dropped onto his knees with a heavy clang, transfixed by two flightless arrows that had cut clean through his Mark IV plate.
Clean through. Loken could still remember Torgaddon’s amusement and Aximand’s assurance… They’re probably ceremonial.
I think this is a really good example as to Ancient weaponry can still be really useful with the right ammunition.