What do you mean by a training collar? Choke chain? Prong collar? Shock collar?
Essentially, ANY collar is a training collar, if you are training while the poodle is wearing it

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Mine wears a flat buckle collar and is perfectly easy to train in it. It wouldn't matter if he wore nothing though, because none of our training involves yanking on his neck.
Training theory has really moved on in the last 15 years, to recognising that reward-based training is more effective, kinder, and more FUN! There are still some trainers who cling to outdated, pain/punishment-based methods, but they are becoming fewer and fewer.
There is a really good trainer who posts great training videos on Youtube; if you search Youtube for Kikopup, you'll find a tremendous amount of really good examples of how to train various behaviours using purely positive methods.
I train with reward-based methods, because I want my dog to like and trust me, to love training, and because I have no desire to crush his little poodle spirit. It is more work for me, but we have a much better relationship because of it ... he works for me because he WANTS to, not because he feels he has no choice.