There are many different approaches to both. Highly dependent on the individual.
However, in terms of using what's deemed as a 'bulking routine,' yes, the same routine can be used during cutting phases. Routines don't HAVE to change for the most part. During cutting you still want to tax the muscle, because that's how you KEEP your muscle while in a deficit.
As a generalization, the further into a calorie deficit one goes, then the total training volume should be cut back some. As you go deeper into deficit, you're not supplying your body with enough nutrients to have a speedy recovery period like you would in a caloric surplus.
But again, it's an individual thing. I've known some people that are able to retain a very high volume while in a deep deficit and not sacrifice muscle. Others have had to cut their volume in half. It's all based on learning what works for your own body.