They are usually used interchangeably but yolculuk is more focused on the transportation side of it.
Also both yolculuk and seyahat are used for long distance trips, at least from one city to another city. (like a travel or a journey) If you talk about short distance trips or travels I would recommend using the word gezi which has a focus on the traveling and sight-seeing sides of it and can be used for both short-distance and long-distance travels.
In sum if you want to make a safe choice use the word gezi for trips and use the words seyahat and yolculuk for travels and journeys.
"Seyahat haziranda bitecek." Translation: The trip will be over in June.
Can you say the trip will be finished in June? Will that be accepted by Duo?
I cannot confirm that Duo will accept the answer. Have you tried it?
"Bitecek." Duo defines it as, "will be over."
Finished in Turkish means, "bitmiş."
On the side of caution, I'm saying no. The trip "will be over" means it is still continuing until June.
"Bitmiş", narrative past suffix -miş means it is finished.
Sorry, I cannot give you a clearer answer.