Depression is an elusive disease. Under the best of conditions, someone who is depressed will understand that he or she is suffering and will seek out help. Unfortunately, most individuals experiencing depression do not recognize that their symptoms are related to a clinical psychological problem. Often friends, co-workers, or family members need to help these individuals identify their depression and seek help.

The most common symptoms of depression in adults include persistent sadness, lethargy, irritability, changes in appetite or sleep patterns, physical discomfort, difficulty concentrating, and/or thoughts of suicide or death. Individuals who experience these symptoms chronically (whether or not they are in response to personal crises) may be clinically depressed.

What is the difference between seek out help and seek help?
As Mr. Micawber says, the difference is one of the amount of effort suggested, the version with "out" suggesting more effort or thoroughness.

I'd like to add that with many of these phrasal verbs which have non-phrasal counterparts, a comparison is almost unconsciously made in the mind of the native speaker with other phrasal verbs which have the same connotations. In the case of "seek out", the idea of getting something into the open or into the consciousness more clearly and with some effort is suggested by the addition of "out" when we compare the expression "seek out" with others such as "pull out", "drag out", "ferret out", "check out", "tease out", "make out", "puzzle out", "figure out", "draw out".

I believe it is the native speaker's easy access to many other patterns with the same adverbial particle with the same (or approximately the same) meaning that gives phrasal verbs like "seek out" that extra little oomph when compared with the simple "seek".

Emotion: smile
vocabulary note
(u;mf) also umph, umphh, oomf. [Etymology: Of imitative origin.] . sex appeal, glamour, attractiveness; vitality
1974 San Francisco Examiner 1 May 35/1 He says I ought to use my 'oomph' to help get BART [sc. Bay Area Rapid Transit] finished. What 'oomph' is the man talking about? Ibid. 35/2 All old World War II types will remember when [url=""]Annie Sheridan[/url] was 'the oomph girl’.
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Very little, Andrei. The 'out' is an intensifier, making the idea of 'seeking' a little stronger, more thorough, more complete, etc.
 CalifJim's reply was promoted to an answer.
 paco2004's reply was promoted to an answer.
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Thank you, Paco!
No, I'm not old enough ever to have heard of the oomph girl. Interesting bit of history, though. "vitality" was the approximate meaning I was going for.

Emotion: smile