The municipal authority writes/says they have used a residential property value/capital basis provided by the Tax Administration to determine the property tax. Is the tax value of the property the same as the tax value that the municipal authority uses as

No, the tax value of the property is always less than the capital basis (or the property value). The tax value is affected by whether the dwelling is your primary or secondary dwelling, whereas the property value is independent of this. If the property is your primary dwelling, the property value will typically be four times higher than the tax value.