To my non-native ears, they always do even though the dictionary says otherwise. Do you say the two words in the same way in your speech?
Additional information that might be useful:
I understand and recognize the difference between the two. It's just the difference seems to vanish in fast-paced native speech. I'm asking about whether native speakers ignore the somewhat subtle difference in their casual fast-paced conversations, and produce the two words/sounds in the same way. I wanted to confirm whether that was true or I was just hearing things.
My native language is Arabic. I can tell whether the speaker's accent is American, British, Canadian, etc., but honestly, both Brits and Americans gave me the same experience. I can determine from context which word is meant. Because my ears are not well-trained to hear a British accent, the difference is almost impossible for me to grasp in British casual fast-paced speech.