Is it right that my new contacts have a higher power than my glasses?

I've had glasses for about 4 months. My glasses prescription reads -0.50 in both eyes. Today, I got fitted for contacts. They examined my eyes, and they got -0.50 in both eyes again. The contacts they gave me were -0.75. Is that correct? I noticed blurry vision on my drive home and when I look at my cell phone screen, it almost has a double-vision effect. I also have a headache. I've had the lenses in for about 4-5 hours now. I called the office, and they said that -0.75 is correct and to give it a week until my follow up appointment to see if my eyes just needed to get used to them. Shouldn't my prescription be lower since the contacts are directly on my eyes and not a few inches in front of them like my glasses are? Does anyone have any feedback or advice?
Added (1). Yes, my glasses are -0.50. I get headaches if I don't wear them. But now I feel like these contacts are too strong

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