理想 and 現実: desired states and actual conditions
Describe the gap between an ideal and reality, and track whether realization is desired or complete.
A desired state
理想, read りそう, is a state regarded as most desirable. 理想の家を探しています。 means looking for one's ideal house.
理想が高いですね。 says that someone's ideals are high. Context identifies the demanding standard; it does not necessarily concern price.
Actual conditions
現実, read げんじつ, means reality. 現実は予想より厳しかったです。 says that reality was harsher than expected.
現実を見て計画を変えました。 means changing a plan after considering reality. It does not say that the plan was abandoned entirely.
A gap and its realization
理想と現実の間に差があります。 says that there is a gap between the ideal and reality. It does not quantify the difference or specify a numerical direction.
理想を現実にしたいです。 expresses wanting to make an ideal real. Distinguish this wish from realization already achieved.
Does 理想を現実にしたいです say that the ideal has already been realized?
Show the answer and why
No. It expresses a wish to realize it in the future.