If you have an IPad, “I’m on my IPad” makes sense. I have not heard people refer to other brands of tablet computers as “Pads.” “Tablet Pad” sounds redundant.

I'm on my tablet

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I agree with John and J. Rios. An IPad is a specific brand of tablet (made by the company Apple). We only use the word "pad" if we're talking about an IPad. Any other type of tablet is just called a "tablet."