Kyle katarns ability sais transfer a token while garven dreis sais gains.

What is the difference, there isn't a transfer topic in the rule reference

Kyle: "At the start of the Engagement Phase, you may transfer 1 of your focus tokens to a friendly ship in your firing arc ."
Garven: "After you spend a focus token, you may choose 1 friendly ship at range 1-3. That ship gains 1 focus token ."

While not stated in the rules reference (EDIT: Stated, but a bit hidden, see below), it seems pretty straight-forward:
Kyle loses his token and gives it to the friendly ship before engaging.
Garven spends his token during an attack (or whatever other effect he might have to spend a focus token) and then the friendly ship gains a token. He can't give the focus token for no reason (downside), but he can use it before handing it over (upside).

EDIT:
See the "Token" topic in the Rules Reference:
"When a ship is instructed to transfer a token to another ship, it is removed from that ship and assigned to the other ship."

(On most PDF viewers you can press Ctrl+F to open up a search window. Super helpful in cases like this where a topic is hidden inside another topic.)

5 minutes ago, GermanBlackbot said:

Kyle: "At the start of the Engagement Phase, you may transfer 1 of your focus tokens to a friendly ship in your firing arc ."
Garven: "After you spend a focus token, you may choose 1 friendly ship at range 1-3. That ship gains 1 focus token ."

While not stated in the rules reference (EDIT: Stated, but a bit hidden, see below), it seems pretty straight-forward:
Kyle loses his token and gives it to the friendly ship before engaging.
Garven spends his token during an attack (or whatever other effect he might have to spend a focus token) and then the friendly ship gains a token. He can't give the focus token for no reason (downside), but he can use it before handing it over (upside).

EDIT:
See the "Token" topic in the Rules Reference:
"When a ship is instructed to transfer a token to another ship, it is removed from that ship and assigned to the other ship."

(On most PDF viewers you can press Ctrl+F to open up a search window. Super helpful in cases like this where a topic is hidden inside another topic.)

Okey thanks, however when a token is tranafered gained or just assigned?

For example, can you trigger jyn erso after Kyle katarns ability?

I would say yes.
The Rules Reference states: "If a ship involved in a transfer is not able to remove or gain the token involved, the transfer cannot take place."
This implies (to me at least) that transfer is a shorthand for "Ship A removes, ship B gains". Therefore I'd say that yes, Jyn Erso could trigger.

You can't transfer a token that has already be spent. In either case, a ship that received the token would be gaining it.

This might help (Rulebook, p. 14)