The complete toolbox
Each link in the chain has its own rules. Here is every method, from the humble Link Cable to the modern cloud.
Link Trade
The original handshake between two carts.
Two games connected by a Link Cable (or, later, wirelessly) swap Pokemon directly. This is the foundation every other transfer method is built on, and it is the only method that is reliably two-way.
Time Capsule
Trade between Generation I and II.
The Time Capsule lets Generation II games (Gold, Silver, Crystal) trade back and forth with Generation I games (Red, Blue, Yellow) - the only time the franchise allowed a brand-new generation to trade with the previous one.
The Great Divide
Where the old world stops.
There is no way to move a Pokemon from Generation I or II directly into Generation III. The jump from the Game Boy to the Game Boy Advance changed the save hardware and the entire data format, severing the link forever.
Pal Park
Migrate from the GBA into Generation IV.
Pal Park is an in-game area in the Generation IV games that imports Pokemon from a Generation III cartridge slotted into the bottom of a Nintendo DS. It is strictly one-way: once a Pokemon migrates, it can never return to the GBA game.
Poke Transfer
The Generation IV to V one-way lab.
The Poke Transfer Lab in Generation V (Black, White, Black 2, White 2) pulls Pokemon up from a Generation IV game. Like Pal Park before it, it is permanent and one-way.
Poke Transporter
The on-ramp into Pokemon Bank.
Poke Transporter is a free 3DS application that moves Pokemon from Generation V cartridges - and later from the Virtual Console releases of Generations I and II - up into Pokemon Bank. It only flows one way: into Bank.
Pokemon Bank Deposit
Two-way cloud storage on 3DS.
Pokemon Bank is the 3DS-era cloud box service. Generation VI and VII games deposit and withdraw freely with Bank, making it the central hub of the 3DS era.
Move to HOME
The one-way bridge from Bank to HOME.
Pokemon Bank can send its entire collection up into Pokemon HOME, but only in one direction. Once a Pokemon moves from Bank to HOME, it can never go back down to Bank or the 3DS games.
Pokemon HOME Transfer
The modern hub for the Switch era.
Pokemon HOME connects the Nintendo Switch games to one cloud. Compatible games deposit and withdraw two-way, but every game only accepts the species that appear in its own regional dex.
GO Transporter
From Pokemon GO into HOME.
Pokemon GO can send Pokemon to Pokemon HOME using GO Transporter Energy. It is one-way: a Pokemon sent from GO to HOME can never return to GO.
GO Park
Kanto Pokemon from GO into Let's Go.
GO Park is a complex in Let's Go, Pikachu! & Eevee! that receives Kanto Pokemon sent from a nearby Pokemon GO account. It is one-way and limited to the original Kanto species (and their Alolan forms).