Most definitely different.
Had= Sounds closer to "hat"
Head= Sounds closer to "bed"
I know of a lot of people who have difficulty with some words such as "cat/ cut", "sheet/shed" etc. It usually is because they did not drag out the sounds from certain words, making it sound clipped and curt.
Maybe you need to lengthen "had" a little longer (e.g. "haa-d") and emphasise the "-ED" at the end of "head".