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I believe the easiest way to explain the difference is something like this.

Accounts Payable would be for invoices you have received from vendors but that are unpaid as of a certain date, typically the end of a month. For example if Ford receieved invoices from their steel supplier on February 15th, but were not due to be paid until March 14th the amount of the invoices would appear as an Accounts Payable at February 28th assuming they were entered into the Ford General Ledger, i.e. financial reporting system.

On the other hand Accrued Liabilities would be for such items as natural gas, water and electric which are a monthly expense, but which invoices are not always received near the end of the month. In my personal situation my water bill is due every quarter so if I wanted to due an accurate personal financial statement for myself I could divide a quarterly water bill by three months to estimate my monthly water usuage. I could then record this amount as an accrued liability - water utility for the first and second month of each quarter until the point that I actually received the bill from the water company, at which point I would pay the actual water bill and what ever increase or decrease from my monthly average would flow through to the month that I actually paid the water bill.

For example: assume my quarterly water bill is $150. I would therefore accrue $50 water utility in months one and two of the quarter and wait for the actual water bill in the third month. If in the third month my actual bill was $200 I would still have a $50 expense in months one and two, but I would have a $100 expense in the third month. I would probably ask why so much different than previous months and might find out that we had extra house guests, washed the cars more or watered the grass.

This was a simple example, but one I hoped you could understand if I related it to your personal situation.

I hope this helps answer your question.

Sincerely,
DMyers8985
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