हिंदी or हिन्दी ?
Is Hindi spelling fully standardized? It seems that some words are sometimes spelled in different ways, especially with "n" sounds.
The spellings are equivalent.
The dot in the word 'हिंदी' tells us that we need to insert a nasal consonant after 'हि' that is of the same family (pronounced with the same place of articulation) as the following letter ('द' in this case).
For त, थ, द and ध which are Hindi's dental consonants, the nasal in the family is न. So, हिंदी is equivalent to हिन्दी.
Among the five nasal consonants in Hindi, न and म (and to a lesser extent ण) are widely used in modern Hindi. So, in words where the dot stands for these nasal consonants, there is flexibility to either spell the word with the dot or with a conjunct consonant. Eg: हिंदी/हिन्दी, लंबा/लम्बा ('tall'), etc.
On the other hand, the other two nasal consonants ङ and ञ are almost never found by themselves in Hindi. As a result, when the dot stands for these consonants, it is retained as a dot and not written as a conjunct. So, अंक ('number') is almost never written अङ्क and व्यंजन('consonant') is almost never written व्यञ्जन.