Are points and closing costs of a new mortgage the same thing?

[PaulaM]

No, they aren't the same thing but lenders often use the language to describe the same costs. A point is 1% of the loan value. It is a cost that you pay to receive a lower interest rate on a loan. It is deductible in the Your Home section. 

Other Items on closing disclosure form that may be deductible:

•  interim interest paid at the time of purchase (the charge at closing would normally be done for interest up to the date of first payment). 
• real estate taxes charged to you. 
• points - On a refinance they need to be amortized over the life of the loan; unless the points were used to improve your main home.
• private mortgage insurance but, if prepaid, only the amount allocable to this year based on an 84 month amortization. 

Other fees, such as commissions, attorney fees, preparation of deed, abstract fees, owner title insurance, recording fees are added to the basis of your home, and not deductible.

https://www.irs.gov/pub/irs-pdf/p936.pdf