In addition to empathiosis' great post:
MSWs training to be LCSWs are generally supervised by LCSWs, just as clinical psychologists are usually supervised by other psychologists, but may, in rare cases, be supervised by clinical psychologists. I don't think psychiatrists ever "officially" supervise anyone but psych. residents (it's a different field, really), but LCSWs, psychologists, and psychiatrists often work together in practice.
About the timeline—it's going to take you more than 5 years to earn become a licensed clinical psychologist. While many programs say that they can be finished in five years, in reality, it often takes more like six or seven (or even longer on occasion), mostly due to finishing/defending/revising your dissertation, but sometimes due to things like getting a competitive amount of assessment/clinical/research experience for internship applications or not matching to internship and having to wait and apply again the following year, Also, keep in mind that most, if not all, states require a post-doctoral (that is, after the PhD/PsyD, including internship and dissertation, is complete) year (~1,000 hours) [maybe empathiosis and I are looking at different states?] of supervised practice until one is eligible to take the state licensing exam and become a clinical psychologist. So, really, you're looking at at least 6 years post-baccalaurate until you could become a licensed clinical psychologist, but probably more like 7 or 8, assuming you got into a program straight out of undergrad., which is somewhat uncommon but by no means impossible.
As far as pay differential between LCSWs and clinical psychologists, it really depends on where you work. The government/military and many agencies will give a higher salary to a licensed clinical psychologist over an LCSW, but it's not as high as you may think. As far as private practice goes, many—but not all—insurance companies reimburse LCSWs, LPCs, and clinical psychologists for therapy at the same rate, and many clinicians choose to run cash-only private practices to avoid having to deal with insurance. From what little I understand of it, private practice is just like running any business, where most of your income ultimately lies in your ability to get/"keep" clients through things like referrals, positive word of mouth, etc. Clinical psychologists can make extra income through doing assessments by referral, but you still have the same issues with referral base, etc.
Both options have their pluses and minuses, based on factors like what sort of training you want (research, clinical, an even mix of both?), your geographic mobility and/or limitations, your financial situation (PhDs are often fully funded while MSWs generally aren't, but funded PhD programs are beyond competitive, and if you go to a non-funded program, you could end up spending more than $100,000 on tuition alone, not to mention the fact that some of these programs have depressingly low match rates), whether you want to do assessments, whether you mind some of the social justice/policy curriculum found in social work (though this may vary depending on the program), how much time you're willing to spend in school, etc., etc.
Hope that helps!
ETA:
Salary differential for a LCSW/licensed clinical psychologist working for the VA in Alaska. (This is Alaska, so the numbers are skewed HIGH):
Psychologist: 68625.00 to 89217.00
SW: 57709.00 to 75025.00
