Title companies do not assess property, at all, ever. By "city or the assessment" I am going to assume that you mean the tax assessment, which could be very different from "fair market value", or a lenders appraisal.
Here are some short definitions:
Tax appraisal - the amount assessed by your local taxing authorities on a property by which your annual taxes are calculated.
Fair market value - what any property will bring in a current marketplace, which is based on many different factors. This could differ from one month to the next, year over year, even week over week depending on market volatility, condition, location and desirability. Also generally stated as "what a buyer will pay and what a seller will accept".
Lender's appraisal - the amount a lender will justify loaning on a given property plus any down payment made by a buyer.
There are a lot of nuances to value. A good Realtor can assist you with questions and help you understand what value means in terms or different assessments.