Advance tax

Advance Tax is payable in respect of all income, if tax thereon comes to more than Rs. 10,000 (including cess)....

About you second doubt..,

As far I think, Tax Payable used when we are making calculation for payment of Advance Tax or Self Assessment Tax..., while Tax liability term used when AO issue demand notice, therein Tax Liability word is uses... 

Although, there is no such technical difference and you can use any of such terms to express what tax you have to pay as advance tax or self assessment tax or demand....