Are Surrey and Yorkshire in the Same County?

No. They are separate historic and ceremonial counties in different regions of England:

• Surrey: South East England, bordering Greater London (southwest). County town: Guildford.
• Yorkshire: Northern England, largest historic county. Subdivided into North, South, West, and East Riding (modern ceremonial counties: North Yorkshire, South Yorkshire, West Yorkshire, East Riding of Yorkshire). County town (historic): York.

They are separated by ~200 miles (320 km) and several counties (Hampshire, Berkshire, Oxfordshire, Northamptonshire, Leicestershire, Nottinghamshire, South Yorkshire).