The English language verbs Intrude and Interfere have similar meanings, but they are different, as I shall explain, using British English examples.
Intrude means to go into a place where you should not be. This could be as simple as causing someone inconvenience by being there, right up to it being illegal to do so. An intruder (noun) is someone who intrudes.
"The cleaner intruded into the important meeting."
"I am having a private conversation, please don't intrude."
"The intruder was caught on CCTV, they turned out to be the burglar we were looking for."
Interfere means to interrupt an action and thereby be a nuisance to someone.
"The old man interfered with the police investigation."
"Please don't interfere with the control panel."
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