The tax rate in one municipality is higher than the tax rate in another municipality.  Does that mean the taxes will be higher in that municipality?

No.  Taxes due on a property depends on 2 things, the tax rate and the assessed value.  They are multiplied to determine the amount of the tax due.

Taxes Due = Tax Rate times Assessed Value

Assume the market value of 2 properties is the same at $100,000.  In one municipality, it is assessed at $80,000, because all property in the municipality is assessed at 80% of market value.  The tax rate is .024 ($24.00 per thousand).  The tax due is $1,920.

In the second municipality, the $100,000 property is assessed at $95,000, because all property in the municipality is assessed at 95% of market value.  The tax rate is .022 ($22.00 per thousand).  The tax due is $2,090.

In this situation, both properties have the same market value, but the property with the lower tax rate has the higher taxes due.