Yes it matters.
And yes it can be confusing because the answer is not clear cut.
The best approach depends on many factors, including:
*your conditioning level: the better your cardiovascular conditioning is, the less stressful on the system the higher intensity methods will be. The less stressful something is, the less cortisol you will produce in response. The less cortisol you produce, the better it will be for your body composition. For example, high intensity intervals might be fine for someone with very good conditioning, but for someone with poor cardiovascular capacities it could be come too much of a stress and do more harm than good.
*what your training looked like: if your lifting workout was very stressful, produced a lot of cortisol, then you might want to stay with lower stress cardio afterwards. Whereas if your lifting session wasn’t too hard or if you didn’t lift, you could do harder with the cardio. For example, I would not use high intensity intervals after a hard leg session but it would be fine after an arm workout.
*the time of day you are training: high intensity intervals lead to a higher adrenaline production than steady state cardio (this is the reason why intervals burn a bit more calories even after the session is over). If you do it early in the day that is not an issue. But if you do it in the evening it might interfere with your sleep, which will end up being detrimental.
So really there is no clear cut answer.
The harder you workout is, the less intense your cardio should be
The later you train, the less intense your cardio should be
The less cardiovascularly conditioned you are, the less intense your cardio should be
When I work with fat loss clients I always prefer to assume that they are not super cardiovascularly fit (I would rather start less intense and work my way up). And start with mostly steady state, lower intensity cardio.
As they progress I gradually start to add intervals in, but less demanding intervals (for example 15 seconds intense/45 seconds slow for 6-8 minutes) and then I progress toward more demanding intervals.
For example… and this is NOT a prescription. It is NOT what I am telling you to do. It is just to illustrate the approach.
Low intensity steady state cardio 20-30 minutes after your workouts
Keep the low intensity steady state for 20 minutes after your workouts, and add 6-8 minutes of intervals (15/45) twice a week, after the LISS.
Keep the LISS once or twice a week (on the hardest workout days). On the other workout days perform 10-15 min LISS as a warm-up than 30/30 intervals for 8-10 minutes.