Just a guess, are there any differences between a police sniper rifle and a military DMR?
Yes. Very much so. Though the definitions vary the general description can be as follws.
Police Sniper
More often and more accurately called a "Counter Sniper". They are usually armed with sniper-grade rifles and ammo with sub-MOA capability and operate as a 2-man team (shooter/observer-spotter). They take their instructions from a team leader/commander who almost always controls their engagement options and usually have attended at least one multi-week outside sniper training course to become qualified as a sniper. They are generally very good in urban environments and proficient position/movement shooters. They usually do not have offensive capability/authority (expect in illawful scenarioes like Ruby Ridge ID) and are reactive/defensive in nature. Most of their training is focused on shots under 100 meters. > 400 meter shots would be rare.
Designated Marksman
These are select military riflemen who are an integral member of a small unit (squad/platoon) and operates usualy alone (w/o a spotter) with that unit as a DM. Often their rifle is a select "accurized" variant of the standard battle (M16/MK12, M14/M21, M16/M110 SASS, HK416/HK417, MK16/MK17, AK/FPK, M1 Garand/M1C/D, etc.) rifle so that he does stick out and become the first target of an enemy sniper. He generally has been through 3-5 days of DM training within his division and has a capability of from 1-2MOA using standard issue ammo but his ability with the variable high magnification optics makes him the eyes of the unit and save the 7.62mm LMG he has the only organic squad/platoon weapon precise enough at long ranges to deal with threat weapons like 7.62mmR PKM's and SVD's. As an experienced member of an infantry squad he would be highly proficient in all environments where his unit is operating. His engagement authority is both offensive and defensive and under cntrol of the small unit commander. Shots at the MER of the rifle (600 m to maybe 800m tops) would be within his capabilities. The EOD precision marksman would fit into this role.
Sniper (Military, SOF)
Specially selected, trained and equipped "talent" assigned to a special role as "sniper/observer". He usually has attended various multi-week sniper courses and as a team is assigned from a larger unit or cell in support of other elements within his overarching oranization. His capabilites are immense usually including call for fire skills, laser target designation, advanced commo skills, anti-materials capabilities, firing from helos, and long term recon training, etc. His weapon is capable of sub-MOA accuracy, he has various types of special purpose ammo available and he is trained on more than just one weapon/caliber. He would be highly proficient in engaging targets at or beyond the MER of the weapon(s) he is qualified on and rules the 800m and beyond portion of the battlefield. He is a combat multiplier who can decide for the most part who lives and dies within his opponents lines and as such is always the first target of his sniper opponent.
Again there are many variables to this and much crossover but in general terms this applies.
G3Kurz