Administrative costs include the fund manager's salary and costs such as record keeping, accounting, mailing prospectuses, customer service and maintaining a website). Though they'll vary, these are not likely to be vastly different from ETF to ETF unless it's a small ETF.
Trading costs can come into play when index components change. This should affect all similar index ETFs relatively equally. However, if there are large amounts of buying or selling of one ETF, it can trade at a premium or a discount to its holdings. To get the NAV back in line, Authorized Participants trade large blocks of fund shares and underlying securities with the ETF manager, arbitraging the two back toward parity. This drives up trading costs for the affected ETF. This hidden cost is lower for ETFs tracking larger indexes but higher for that involve a narrower sector.
Large indexes can have many components. For example, the Russell 2000. It's cost prohibitive for an ETF to duplicate all of the holdings so they build a representative portfolio with a sampling of stocks that best mimic the performance of the index. A sampling ETF will have a lower expense ratio than one that tries to duplicate identically. Conversely, an index like the S&P 500 is comprised of the largest and most liquid stocks sp there's full replication.
The short answer to why expense ratios vary is that it depends on different variables.