I have done this before (move to another state). Federal taxes will be the same. State taxes will be divided up between the two states dependent on the time you were in each.
For example if you were in Utah for 3 months from January before you moved, and then you were in Kentucky for 9 months, then you would pay 3 months worth of Utah taxes and 9 months worth of Kentucky taxes - for state taxes only. (Note: you would pay taxes for the 3 months of income in Utah and for the 9 months of income earned in Kentucky - do not divide your whole year's income into 3 and 9 months unless your income stayed exactly the same. Most tax software will calculate this automatically if the software is any good.)
New York to Maryland is not that dramatic of a move, but it sounds like your taxes and cost of living may decrease.
There are other factors though, the hidden taxes. A hidden tax is car registration and taxes. Some states make you pay car taxes or property taxes (for owning a car) in the new state when you move. Car registration fees may increase, increasing your effective "tax". Other hidden taxes include tolls, parking tickets, speeding tickets (an avoidable tax), license fees, unknown sales taxes (e.g. California has a tax on soda that is automatically applied if you buy it, you may miss this tax if you don't look at your receipt), and many more.
But, overall, since New York has some of the highest taxes in the country, then a move to any other state, with the exception of California or Hawaii, will likely result in a net decrease in taxes as well as a net decrease in living expenses for the same standard of living, after you conclude your moving expenses - unless perhaps you move from a very rural part of New York to a high-priced part of Maryland.