It's not profession-specific - counsellors do therapy, and psychotherapists do counselling - its more about figuring out what you personally need right now. Where it can be difficult is if you start a more intense, ongoing therapy and can't continue it. That can feel like you've opened things up and are then left to deal with the fallout - and make things worse, not better.
People often question therapy as being unduly long, and ongoing therapy can be seen as an indulgence. And of course, it can be expensive. But ongoing and open-ended doesn't necessarily mean years, it just means you're able to take the time you need.
From that freedom to choose how long you stay comes the ability to more freely express yourself, which openly builds trust, enabling us to receive and hear at times challenging feedback, and feel difficult feelings.
In contrast, with a shorter-term treatment, it's best to have a very clear goal of what you want to focus on - stress management, reducing your drinking, particular problems at work or some skills to better manage anxiety - for example. And to also be very clear with the therapist you're seeing that you are unable to self-fund beyond the few sessions that are funded so you do need to focus and work towards some practical solutions.
That may mean not talking so much about the past, or wider issues in your life. That can be challenging but it is possible to get quite a lot from just a few sessions, and often it can leave us with tools to go on practising and a focus in our own efforts to make changes in our lives.
And while I do understand that sometimes you just absolutely can't afford it, it is worth challenging yourself as to what you value. Some people choose to attend fortnightly, negotiate lower rates or access community services where the fees are lower, even if there is a wait.
While in the ideal world no one would have to pay for mental health treatment that they need, we don't live in that world (yet). But if you know what you need, and after trying a few sessions if you feel like you need more, then I'd encourage you to move heaven and earth to make that happen.