Not an expert, just someone who looked a few of them.
AX - original target was larger size manufacturing companies, began in Europe, competed with Navision on the fringe of the mid/high market. both introduce graphical interface and easy customization to the market, before this everything was charater based and not very flexible.
NAV - orginal target mid market retail/wholesale distribution companies, too big for quickbooks, mas90 ect but not big enough for Orcle or SAP implemention - began in Europe little penatration in the USA as first
GP - Same basic market as Navision but primary the US market.
SL - Soloman - same market as GP and NAV, began as charater based and evolved alone the same lines as GP
Navision bought AX with goal of combining and try to reach the low end of the high end market such as Oracle and SAP.
Microsoft entered US market with GP purchase and expanded to Europe with Navision/AX purchase