Secure and sure, along with a handful of other words originating from those terms, share an etymology. These words are listed and defined in this post.
The parent word is the Latin adjective securus, meaning “free from care or danger.” (The first element, se, means “free from” and is seen in secret, and the second is a form of cura, which means “care” and is the source of cure.) Secure is both an adjective meaning “safe” or “fixed in position” and a verb meaning “to make safe or fixed.” The noun form is security, extending in meaning to refer to a financial asset or document. The antonymic forms are insecure and insecurity, which also pertain to self-doubt; secure and security are also used in psychological contexts.
Sure, from securus by way of Old French, means “confident,” “firm,” or “reliable” or, informally, is a substitute for certainly or “don’t mention it” in response to a request or an expression of gratitude; the antonym, in the more formal senses, is unsure.
Idioms with sure as a foundation include “for sure” (“certainly” or “without a doubt”) “sure enough” (“certainly”), “sure-footed” (“confident in movement”), “sure thing” (“certainly”), and “to be sure” (“admittedly”). “Sure thing” is also an idiomatic noun phrase pertaining to someone or something that is certain to succeed; the phrase “sure bet” is synonymous.
A surety is a guarantee, and insurance refers to a guarantee of protection or safety. Assurance can also refer to a guarantee (including, in British English, what is referred to in American English as insurance in the sense of a contract guaranteeing protection against loss), but it also pertains to security or to confidence (as well as overconfidence). The noun ensurance is obsolete.
Although there is some overlap in the meanings of these words’ verb forms, most writers observe the following distinctions: to assure is to convince, to ensure is to guarantee, and to insure is to make certain or safe. Meanwhile, reassure means “assure again” or “restore confidence,” while reinsure means “insure again”; there is no equivalent prefixed form of ensure. Similarly, one can be (better yet, remain) unassured and can be or remain uninsured, but unensured is rare.