Hello Wendy,
'Ideal' is a conception of something that is perfect and that one seeks to attain.
'Dream' is a cherished hope, ambition coupled with a strong desire to achieve something.
In both cases of 'ideal' and 'dream', there is something unattainable and one seeks to obtain or achieve that thing.
However in the case of 'ideal' it is more realistic and has the attributes of perfection ( relatively spoken for the seeker).
It could represent the best example of something you can think or imagine.
"She represented his ideal of beauty."
Ideals could also be ideas about good and right,that one tries to follow in life.They are exemplar for the seeker and represent a state of perfection.
"He has high ideals ,but often fails to live up to them."
In the 'dream's ' case ,it is more of a fantasy, tends to be more unrealistic ,but still one hopes to realize it in the future.
A dream home or a dream vacation are in one's mind a bit far-fetched for the moment, but could be attainable in the future.
'a dream' could also refer informally to something or someone that one likes very much as in:
" She is a dream."
"Driving this car is a dream."
It is attainable in those cases, but represents something so desirable and fantastic ,thus comparable with a dream.