Usually, most nouns that are derived from verbs are formed by adding “er” to the base forms.
Examples are farm (=farmer), preach (=preacher), see(=seer), love (=lover), drive (=driver), program (=programmer), work (=worker), believe (=believer), etc.
But this is not always the case. For example, someone who cooks is called a cook, not a cooker. A cooker is an appliance used for cooking food, typically consisting of an oven, hob, and grill and powered by gas or electricity.
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In the same vein, someone who gossips is called a gossip, not a gossiper. Also, a person or organization that sponsors something or someone is called a sponsor, not a sponsorer.
We must also bear in mind that an assassin is the correct word for someone who murders a specifically targeted individual, usually for religious or political reasons, not an assassinator.
According to the definition by most dictionaries, assassinator specifically refers to someone involved in an actual and successful assassination i.e. the culprit to a murder case. Assassin pertains to someone employed to kill people (regardless if they have or have not yet successfully assassinated anyone in the past.
