As an ophthalmologist and a psychologist, I do indeed have experience with both da Eyes and da Feelz.
Let’s clarify terminology first. A psychiatrist is an individual who has graduated from an accredited med school (MD or DO), and then completed a four-year training program (the generic term for post-med-school training is residency) in psychiatry. So with few exceptions (notably certain international graduates), a psychiatrist did a 4-year baccalaureate in something, then got an MD or DO (another 4 years), then completed a psychiatry residency (yet another 4 years).
On the other hand, a psychologist is someone who has a terminal degree (PhD or PsyD) in psychology. S/he did a 4-year baccalaureate in Psychology (usually), then completed a Psych PhD program (usually 5 years) or a Psych PsyD program (usually a year or two shorter). Assuming his/her graduate studies were in clinical psych (there are many other, non-clinical psych fields; eg, experimental psych, which is what my PhD is in), s/he will be eligible to work as a licensed clinical psychologist in most states.
What’s the difference between a psychiatrist and a clinical psychologist? Chiefly it is the reliance on medications in managing pts. Psychiatrists, being physicians, are licensed to prescribe meds, whereas in most states the prescribing abilities of the (non-physician) psychologists are limited (if they have any such rights at all). Thus, psychiatrists tend to focus on psychopharmacological treatment, and psychologists tend to focus on cognitive/behavioral therapies (although many work closely with a psychiatrist, who will prescribe meds for a given pt as needed).
One of the biggest hurdles to becoming a psychiatrist or a psychologist is simply gaining admittance to the respective training programs (ie, med school for psychiatrists and grad school for psychologists). Admission is generally quite competitive, requiring both high undergrad GPA and admission-test scores (MCAT for med school; the GRE for grad school).
As for ophthalmologist vs optometrist: Both specialize in eye care. However, like a psychiatrist, an ophthalmologist is a med-school grad, but in this case his/her residency was in ophthalmology. An optometrist is akin to a psychologist–s/he got a bachelor’s degree in something, then went to ‘grad school’ in optometry. Optom school is 4 years, and culminates in the awarding of the OD degree (note: not the same as the DO mentioned above). In terms of scope-of-practice, ophthalmologists can prescribe any and all meds (in some states, optoms have limited prescribing rights). Further, ophthalmologists are trained in eye surgery, whereas the vast majority of optoms are not. As a practical matter, most ophthalmologists spend their time doing surgery and managing diseases of the eye (eg, glaucoma; diabetic retinopathy; ARMD), whereas most optoms spend their time checking people for glasses and contacts.
In terms of gaining access to training, optometry school is much more accessible than is an ophthalmology residency.
All that said, I have no idea what @planetcybertron should go into. I will say that, as a practical matter, any such decision should be made in light of how attractive a candidate one is vis a vis gaining admission to the requisite training program. Further, the issue of training time should be considered–psychiatry is a minimum 8 years post-undergrad (longer if one wishes to subspecialize; eg, Child Psychiatry).
Happy to answer questions if anyone actually read this wall of text.