Oilfield Service Company is a company which provide services / support to the petroleum exploration and production industry but do not typically produce petroleum themselves. The servicing companies specializes in providing upstream services to the clients such as
1. Seismic & geophysics
2. Reservoir engineering, simulation & consultation
3. Drilling & measurement
4. Wireline & well testing
5. Completion
6. Production
7. Well intervention

Drilling contractor is the company that owns and operates a drilling rig.

Most of the cases, drilling contractors own the rigs and provide the drilling services (exploration/development) and some of the rigs are capable doing the well intervention works. Not only that, with the current market, some of the rigs also willing to contract the rig ONLY for ACCOMMODATION/HOTEL.

Oilfield service companies, on the other hand provide the specialists, tools and technology to achieve the campaign's objective.

For example (in normal case);

Client:- Shell/PCSB/EXXON etc ; contracted
Drilling contractor : Transocean/Seadrill/Maersk Drilling (i.e Jack up Rig / Semisubmersible Rig/Drillship) - The rig packages are often offered as it is and sometimes require to do upgrades depending on the client's requirement on the drilling campaigns.

Client also contracted;
Service companies to provide;

Slb / halliburton /Baker etc: MWD/LWD; DD services (crew & tools/equipment)
Slb / halliburton /Baker etc: Wireline services (crew & tool/equipment)
MI Swaco/Scomi etc : Drilling Fluids services (crew & materials)
Geoservices/DHI/etc: Mud Logging Services (crew & monitoring equipment/sensors)
SLB/Baker/etc: Hole opening, Fishing services, etc (crew & tools/equipment)
WTFD/Franks/KST : Tubular running services (crew & tools/equipment)
WTFD/HAL/BH etc: Completion Services (crew & tools/equipment)
FMC/etc: Wellhead Services (crew & tools/equipment)
Oceaneering /etc: ROV services (for floating rigs)