What types of BB-axle to crankarms interfaces are there?
When comparing BB types, a significant factor to consider is the longevity of the bearings, and serviceability. Outboard bearings have the most longevity but are essentially unserviceable. When they go, or when the splines are too damaged by bad installation/removal or inferior tools, then toss them and buy replacements. Outboard BBs are used with Hollowtech (Shimano) and Ultra Torque (Campagnolo). Then there are press-fit BBs, in which the cups (or a sleeve into which the cups are fit) are pressed directly into the BB shell, which is now made without any threads. These need specific tools to install and remove, but are preferred for high-end bikes.

The BBs with the least longevity and least serviceability are ISIS (ten-splined). These are also a pain to remove the cranks from, since you need a special attachment on your crank puller (similarly with octalink, incidentally). The reason these have such little lingevity is that the diameter of the spindle means that the bearings contain much narrower balls. I'm not sure what gauge, but if you've ever taken apart bearings on a bike, there are three main sizes: BB, wheels and headset, in order of size from largest to smallest. The BB should have the largest because there is significantly more torque applied to the BB that anywhere else on the bike. The headset for example endures comparatively little. Isis BBs have to fit the bearings and the thicker spindle in the same shell size, and so they use smaller bearings that can't endure as much torque.

As for the most serviceable: older bikes, before they invented cartridge BBs (of which all the above except outboard bearing style are examples), had loose bearings (or at most inside one-sided cages) sitting between the cups (the sides that screw into the BB shell) and the cones (raised smooth edges on the spindle itself). These cup-and-cone BBs are analogous to the internal design of the wheel axle and bearing setup. These require frequent (every 1000km or so) disassembly, cleaning and reassembly as they get fairly full of crud. On a recent clean of an older fixie I run, I found that I had split several of the bearings into chunks, explaining the crunchy feeling of my rotation. As loose bearings are readily available, these older style BBs can be continued to be serviced right up until the cups and cones themselves get too degraded on their inner surfaces to function properly (pits in the grooves for example, where the ball bearings will naturally sit in, and which come about through over-tightening) will mean that ball bearings will wear out quicker.

Square taper BBs, as the commenters note, come in several incrementally different types. The main difference between ISO and JIS is the length of the tapered section of the spindle. ISO is shorter. The angle of the taper is the same (I believe), so you can fit an ISO crank on a JIS taper (and I have done this) but the cranks sit a couple of mm further outboard than ISO > ISO or JIS > JIS. Conversely, you could fit a JIS crank onto an ISO BB, but depending on the spindle width, it may rub against the BB shell as it would sit a few mm inboard.

As far as ease of installation, longevity, ease of crank installation and interchangeability, I would definitely suggest that outboard bearings, either hollowtech or ultra-torque, are the best balance of cost and benefit.