终止 is formal and definitive — something ends completely. Compare: 停止 (tíngzhǐ, to stop — can be temporary), 中止 (zhōngzhǐ, to suspend — implies possible resumption).
usage
Note: 终止 (zhōngzhǐ, to end permanently) and 中止 (zhōngzhǐ, to suspend) are homophones but mean different things! 终 = final end; 中 = in the middle.