Formal philosophy is a bit like chess: It’s been around a long time, it has a set of established rules by which you play (e.g. with few exceptions, “moves” are to be firmly grounded in logic and reason), it takes a long time and a lot of practice to master, there are standard “openings” (e.g. The Ontological Argument for the Existence of Deity), and a minor change in reasoning can have logical implications that create a “whole new game”. But, by far, the most important of these characteristics is that each premise (or conclusion) must be firmly established in logic and reason.
That’s the case with formal philosophy, but it’s not the case with street philosophy. In street philosophy, it’s perfectly OK to base your conclusions on how you feel about something, on guesses, on hunches, on evidence available only to you, on faith, and so forth.
In my experience, a formal philosophical conversation is often about as lively as a chess match. Lots of long pauses for weighty consideration between “moves”. Street philosophy, on the other hand, is much more lively.