What is the difference between on-chain scaling and off-chain scaling? What is on-chain scaling and off-chain scaling?
What is the core difference between on-chain scaling and off-chain scaling?
Note, I use scaling, capacity, and scalability as follows:
Scaling: Growing the network's utility in any fashion.
Capacity: The number of transactions that can be processed on the network.
Scalability: Capability of the network to handle a growing amount of work.

On-chain scaling
The term &quot;on-chain scaling&quot; is frequently used to exclusively refer to increasing the blockchain capacity by means of bigger blocks.
However, in the literal sense of the term, it should refer to any sort of protocol change that improves the network's capacity at the blockchain layer, including changes that facilitate production of equivalent transactions at lower cost. These approaches tend to provide at most a linear capacity increase, although some are also scalability improvements.
Examples:

Blocksize/blockweight increase
Faster blocks
The witness discount of segregated witness
More efficient new address formats
Smaller size of Schnorr signatures
Cross-input signature aggregation
Key aggregation

Off-chain scaling
The term &quot;off-chain scaling&quot; refers to approaches that increase the utility of the network without touching the blockchain, or by making superlinearly efficient use of the blockchain load they produce. I also include approaches that create non-equivalent transactions that result in more efficient use of blockspace.

Batching multiple payments into one transaction
Virtual payments within the system of a custodian (Tipbots, Coinbase,…)
Payment Channels/Tumblebit/Lightning Network
Sidechains
Colored Coins

Generally, off-chain solutions are scalability improvements but go hand-in-hand with a different trust model and different trade-offs. They often require additional software and complexity over on-chain scaling approaches.
For example, Lightning Network will require its users to be online to receive payments while on-chain transactions allow passive receival. On the other hand, it will easily scale the count of payments between participants, but only scale the number of participants in a limited fashion as becoming a LN user requires on-chain transactions.