what is the relationship between tax liability, tax expense, current tax liability and current tax expense.

I learned from the questions that: taxable income* tax rate= tax liability= current tax expense.

But I am still confused a little bit. Could you explain it further? Thanks so much

Hey topzjj,

This actually is not too difficult of a concept. 

Your tax expense is the sum of two components, your current tax
expense and your deferred tax expense.  Let me explain:

In many circumstances, your net income under GAAP will not equal your
taxable income.  In some cases this is due to temporary differences, which
means that the revenue or expense will eventually be recognized under
both methods, just not in the same period.  A good example of this is tax
depreciation vs. book depreciation.  Tax depreciation is often accelerated,
so you would recognize more depreciation expense early on under a tax
basis than a GAAP basis, but you will still eventually recognize that
expense under both methods.  A permanent difference will never be
recognized under one of the methods.  For example, certain GAAP
revenues are tax exempt so they will never be included under taxable
income.

When there is a TEMPORARY difference between GAAP income and
Taxable income, you have to recognize a "Deferred Tax Asset" or a
"Deferred Tax Liability."  If the temporary differences decrease taxable
income in the current period, then they are recognized as deferred tax
liabilities, because they increase the amount of tax that will need to pay in
the future.  If the temporary differences increase taxable income in the
current period, they are recognized as deferred tax assets, because they
decrease future taxable income.  The deferred tax assets or liabilities are
equal to the amount of temporary difference times the expected tax rates
in the years that the temporary difference will reverse. 

Tax Expense = Current Tax Expense plus Increase in Deferred Tax
Liability minus Increase in Deferred Tax Asset.