True value vs. assessed value
True value is market-value concept; assessed value is the taxable value carried on the municipal assessment roll.
New Jersey example
A $300,000 assessment in a municipality assessed near 54% of true value should not be read as a $300,000 market-value opinion.
Official source
https://www.nj.gov/treasury/taxation/lpt/localtax.shtml
This is a plain-English summary. Rules and dollar amounts change, so check the official source or a professional before you file or sign anything.