In German law, the term “Interesse” is only used when dealing with harm and to what extent compensation is owed. So, in contract law, the “Äquivalenz- or positives Interesse” is relevant whereas in tort law, it is only the “Intergritäts- or negatives Interesse” (cf. Grüneberg, vor § 249) that is compensated.
The English term “interest”, on the other hand, refers to a legal or equitable claim to or right in property (cf. Black’s Law Dictionary). It is frequently used in the context of referring to a right in or over land, the two most important of which are the freehold and the leasehold interest (cf. Oxford’s Law Dictionary).
As can be seen, the terms are used in different areas of law and have different meanings. Using them as equivalents when translating would lead to misunderstandings. The appropriate translation will always depend on the context, but for “interest”, in the sense of an interest in real property, we would suggest using “Recht an einem Grundstück” in German, while “Interesse”, could be translated as “(amount of) contractual damages” and “(amount of) damages in tort” respectively.