I suppose they're similar but not the same.
One difference is, the difference between "cause" and "condition". For example, for a plant to grow, it needs a seed, rain, sun, soil, to be undisturbed, and so on. Is it true to say, for example, that "the soil caused the plant to grow"? I'd say maybe not: instead of the soil being the cause, maybe the seed was the cause ... or maybe the sun ...
To avoid that kind of [slight] misunderstanding, I think it might be more accurate to say that these are "conditions" rather than "causes": that the plant grows "on condition that" it's sunny, that it rains, that the soil is good, that there's a seed, and so on.
So I prefer "condition" instead of "cause".
I find that people also sometimes use "condition" as a verb, even though that's slightly inelegant or uncommon in normal (non-Buddhist) English: they say for example, "the rain conditions the growth of the plant" (instead of "the rain causes").
For I think a similar reason people say "depends on" rather than "caused by": i.e. a plant's growth (and thus the plan't origin or coming-into-being) depends on sunshine, even if it isn't caused by sunshine.
The second difference is, what is it that is being caused or conditioned? When people talk about "dependent origination" based on the Pali canon, I think they're often talking about the 12 Nidanas (the topics of which include Ignorance as a condition of Birth of Death), or maybe the 4 Noble Truths (including craving as a condition of, or origin of, suffering, ad the origin of cessation of suffering).
Conversely I suspect that in a biography of Milarepa, it might be that the term is used to describe the causes or cultivation of boddhicitta.
If that's so then perhaps the "cause" that's mentioned is closer in meaning to the Pali word Bhavana.