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The way I visualize how the particle は works is that it opens a giant circle underneath the word it is attached to wherein you can discuss things related to it.

Sort of like this: This

When I use ば I sort of visualize it in the same way... like I am attaching a giant circle to a hypothetical situation as exemplified by the 仮定形{かていけい} form and then talking about possibilities within it.

So I want to know... are they related in any way?

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Yes, they are. The conditional ば is just a voiced version of the particle は. See page 273, on the bottom. See also p.329.

The second seems to be a more recent coining, but it illustrates the principle:



Both are possible, and mean the same.

By the way, 仮定形【かていけい】 is the modern term reflecting its current usage (only with ば). Its historical name is 已然形【いぜんけい】 ("Perfect", as in finished), reflecting how it signified completion. You could say 「我【われ】、忘【わす】るれや」(have I forgotten?) or 「言【い】えど」(=言う けれど). See p.142 of the book linked above.

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