Question about Assessed Value vs. Market Value...

[Mark K.]

Hello, I am a newbie and about two months in.  I've been reading everything I can get my hands on and feel it's time to start analyzing deals and crunching numbers.  I figured I start at the Assessor's site which I did and now have some questions...

• If you look at the two properties below, one an apt building and the second a SFH, why are the Assessed and Market values so far apart for the apt building?
• Using the Assessor's site in NYC, I was able to find Market Value for my building and any condo's.  For Montgomery County, MD, I did not see Market Value so I just used Zillow.  Does Market Value on Assessor's website just depend on your location?  If not, where should I go for Market Value?
• When you are doing your due diligence, at what stage in the process do you look up Assessed/Market Value?
• For Assessed Value, is there anything I would use this for other than when factoring property taxes?
• For Market Value, is this just nothing more than a projection/gauge of the property's value on the market?  What would I actually use this for when analyzing a deal other than a benchmark for comps?

I looked up the apt building I live in in NYC (Manhattan - East Village).  Below are the values, I don't understand how they can be so far apart.  

• Assessed Value (Period begin 1/1/15): $652K
• Market Value (Tax Year 14/15): $1.44MM

Additionally, I also looked at my childhood home in Montgomery County, MD

• Assessed Value (2014): $402K
• Market Value (from Zillow): $451K

Thank you in advance for your help!