Bitcoin is the first massively distributed database. In order to get as many nodes to participate as possible, each node receives some "coin" for participation with a special bonus for early participants to the network. Each node also has the possiblity of initiating a transfer of coins via a cryptographically secure method. Because of controlled supply, increased demand creates a higher price for the coins.
This is all that Bitcoin 1.0 contains. The original plan for Bitcoin was largley derived from Nick Szabo's Bit gold, which is a discussion of how a digital token could be a "store of value." "Gold" is used primarily because it is a traditional store of value vis-a-vis state-issued fiat currency which often has inflationary properties. Via design it is meant to be a 'trustless' alternative to nation-state currencies.
Problems with Bitcoin 1.0 are that the incentivization scheme is highly geared towards very early adopters but that this same scheme works less well later on, the in-network token has no inherent value and is extremely volatile, the real utility of the network (besides speculation) is limited to narrow use cases like international remittances, and the fixed scaricity applies to any given implementation but not the source code. In other words, despite being a very interesting technological innovation, it solves relatively few actual problems.
Bitcoin 2.0 includes the development of an additional degree of possiblities on top of the Bitcoin protocol. Generally speaking, it's things that make use of the in-network "coin" to do more advanced features than simply transfer value. Common features of 2.0 protocols are things traditionally associated with financial markets like futures, derivatives, betting, securities offerings, etc. For the more advanced platforms (which include their own scripting language) this can include things like organizations that exist entirely on the blockchain and which have some sort of internal voting mechanisms.
Within all of these solutions there is a natural tension between the incentivization necessary to the encourage node participation (which must exist indefinitely to maintain network security), incentivization for founders to complete intended goals, the "store of value" proposition, and the "use value" of any given token on the network.
So far 2.0 platforms have not managed this differentiation particularly well, often conflating the different parameters into a single in-network currency. Somewhat ironically, these also frequently present tendencies towards extreme centralization and oligigary, insofar as there is zero necessary transparency at the decision making level for these organizations.
Despite this contradiction between appreciating asset (stock) vs. stable asset (gold) vs. commodity with use value (wood), many of these platforms have managed to achieve a certain level of traction. My anticipation is that the value proposition needs to be ironed out to avoid these various pressures.
For many of the platforms that attempt to offer some internal use value it is highly desirable that they clearly differentiate between "cryptoequity" (appreciation) and use value (desiarably low) and potentially don't rely on any sort of mining related incentivization, which has its own associated problematic features.
This is a strong argument for using some traditional equity structure (either a distinct cryptotoken or a traditional legally guaranteed stock offering) as the base unit for the early user and founder incentivization, while having a in-network currency be derived from use-value and deliberately kept cheap.