To end is to cease something or to come to a conclusion. Stories end, days end, and lives end. The things themselves, in these examples, have intrinsic beginnings and endings, and to end is a natural, organic outcome. Terminate suggests an immediate or abrupt stop imposed upon something, often by impersonal forces. It has a more official and technical feel. A contract, agreement, or license may be terminated before its expiration date. A judge may rule to terminate parental rights. To cap it all off, two extended senses of terminate have emerged: terminating someone can either mean to fire them or to assassinate them.
For talking about things physically extending far down or far back in space, deep is almost always the appropriate word (a deep well, deep shelves, a deep cut). Profound is more elevated diction reserved for awe-invoking depths (profound depths of the sea). Both adjectives can also be used figuratively, of feeling and thought: we admire the deep thinkers and profound poets for their ability to penetrate beyond surface impressions and discover truths inaccessible to most of us. However, deep is more informal and used in this way can come off as a bit sophomoric (Wow, that’s a deep poem.) Profound suggests with more authority something’s intellectual significance (profound ideas or insights). In general usage, profound is most frequently used to describe change and its effects. In this context, profound implies far-reaching, transformative, significant, fundamental, or lasting (profound change, profound impact, profound influence).
The adjectives controversial and contentious both describe something that provokes differences of opinion or disagreements. A controversial issue, statement, or decision is one about which the public has strong and divergent opinions, often longstanding and much-discussed, and not likely to be reconciled any time soon. A contentious issue or topic is one that causes conflict or strife, whether in congress, in court, or at the dinner table. A contentious debate or election, or a contentious relationship with your supervisor, would be marked by hard-fought disagreements, as would a contentious divorce or contentious custody dispute. A controversial figure is a public figure who does or says controversial things. Contentious people are simply argumentative types.