(IMC of course)
Lower-case 'a' assassins are just anybody who kills people, usually covertly, for money.
Capital 'A' Assassins are members of a secret...ish society with rules, hierarchy, and traditions. They're represented by the Assassin PrC as presented in the DMG, spellcasting and all.
You can hire someone to whack your enemy, and whether or not they have any spellcasting abilities, death attack, etc, all depends on the person you hire. If you retain the services of the Guild of Assassins (who'll have an appropriately spiffy name), you can be pretty darn sure the people who do the job will cast spells, not poison themselves, and have access to death attack. On the other hand, you'll probably never meet the people who do the actual killing, just their middleman.