Is there a difference?? I sometimes mix up the two in "reading" practice.

Nick's links to the sounds give

http://www.skritter.com/sounds?file=che1.mp3
http://www.skritter.com/sounds?file=chi1.mp3

I find these (and zhe, se, etc.) quite difficult too.

I find my lips go forward with the chi/shi etc sounds, and not so with the che/she sounds. Also say shi with more of a 'ur' sound, and the she sounds with more of a schwa/ə. Not sure if that helps.

Not sure if it will help， but for the chi my lips also go forward like Byzanti. As for the che, I tend to open my mouth a bit wider.

I always think of che with an 'uh' ending sound and chi as an 'ir' ending sound. I think shi is kind of unique with that final sound off the top of my head?

Good example of pinyin being a bit deceptive and not properly communicating the sounds?

Stuff like dun also. You wouln't think looking at the pinyin that it should have a sort of 'w' sound in it...

For what it's worth, I consider the 'i' of shi, chi, and zhi as being the vowel equivalent of an 'r'. And yes, my lips also go forward with it.

Those urls make it handy to compare the two side by side, thanks for that!!

On a side note, I think I do automatically say them differently without realising I was doing it.

According to the descriptions in the 普通话水平测试实施纲要：
The ‘e’ in che is the close-mid back unrounded vowel [ɤ].
The ‘i’ in chi is 舌尖后不圆唇原音 (a back apical unrounded vowel). 口略开、展唇、舌前端抬起和前硬腭相对。(Mouth slightly opened, unrounded lips, the tip of the tongue against the (front) hard palate.) 发音时、声带震动、软腭上升、关闭鼻腔通路。(The vocal cord vibrates during articulation; the soft palate rises up, closing the passage way into the nasal cavity.)