I think these two words are abused, that's why I seldom use them. Let me break it down from a relationship perspective. . .
In the broadest sense, an 'insecure' person is someone that distrusts his/her partner or doesn't feel comfortable with certain 'moves', especially with the opposite se.exx right? Ok.
Trust, on the other hand, presupposes that a partner is infallible; in other words, him/her can never yield to any temptation from the opposite s.ee.x right? Ok.
Unfortunately, there is a hidden dimension to these two words. When a partner accuses you of insecurity, then it proves your suspicion(s) right. What s/he wants is for you to turn a blind eye, 'leave it for God', or accept the likelihood of their misbehaving as 'one of those things', then you'd be seen as secure.
Trust. When you voice suspicions and all s/he does is lash at you for not trusting him/her, thats a red flag. Do you really think your partner is Jesus? (even He was tempted and only his Godly grace saved him). So what or who are they to make them feel you MUST trust them? Really 'trust' simply means you should free them to do their dirt since 'that's life'.
Truth is, no one is ever 'all that' enough to think s/he's everything a partner wants for ever. Also, no one is ever 'virtuous' enough to be beyond yielding to temptation. As such, 'insecure' and 'trust' are baseless words used (often subliminally) for blackmail and deceit. Only deep thinkers would agree with me.