ASME Sec-VIII

The most basic answer for the differences between Div 1 and Div 2 is that Div 1 is more based on design by rule (cookie cutter formulas) and div 2 is design by analysis (more rigorous calculations involved). And a rule-of-thumb is that Div 1 covers up to 3000 psi, however, it can be used for higher with alternate rules/formulas. Div 2 covers from 15 psig upwards to generally "high pressure" vessels (note that it doesn't explicity give an upper limit) but Div 3 is generally used for high pressure ~10,000 psi.

There are also numerous differences regarding material testing, NDE requirements, experimental stress analysis, user specification required, professional engineer required, allowable stresses, ......

In short: Div 2 provides a better engineered vessel with calculated stresses closer to real stresses, combined with more rigorous testing, allows for savings in material costs (thinner parts may be used) - this is particularly important for larger vessels, but the costs may be offset by the more rigorous design/testing requirements; and some large EPC companies limit high-risk/lethal vessels to Div 2.

I would suggest digging more into this topic and possibly buying some papers off ASME to get a better idea.

You only have to follow any local laws/regulations, company standards, or purchase specifications.