In the US, you must be bar certified in the state in which you wish to practice. Almost no states allow sitting for the bar without a JD (or if you have an LLB from a different country, an LLM), those that do tend to make it nearly impossible as a practical matter. Most US law schools offer an LLM for foreign students with undergraduate law degrees who wish to practice in the US.
Each country will have a different scheme so proceeding with this question without knowing the jurisdiction is a bit silly. I'm guessing you are in the UK or some colony that still respects the Crown to some degree.
As noted, the US doesn't have the barrister/solicitor distinction.
BTW a JD is a 3-year graduate degree (technically a doctorate, but there's no dissertation so its more like a really intense masters in practice) that you can't start until you've completed a 4-year bachelors degree. An LLM is a 1-year masters degree that is ordinarily taken after receiving a law degree in a different country (and at some schools serves as a means for US JDs to specialize in a particular field). An SJD is like PhD (classes + dissertation) but for Law, it is a US degree aimed almost exclusively at foreign legal academics (US legal academics need only a JD).
In many other countries a Law degree is an undergraduate degree (4 or 5 years I think) and no graduate degree is required to practice.