"Vivienda habitual" is used in Spanish as a distinction to "vivienda vacacional". The reason that this particular distinction is made in Spanish is that there are different types of contract, the holiday let can only be for a maximum of 11 months and the lease agreement is for a minimum of 3 years, extendable to 5. For the latter, the landlord is not able to give the tenant notice within these 3 years. If the lease agreement is terminated, it must be on the tenant's behest within the first 3 years.
It is therefore not necessary in English to explain that it is the property of habitual use because the alternative to a property lease agreement is a holiday let/rental.
Usually, "residential" is used in English to distinguish one of these rentals from a "commercial" one so you may like to specify that it's residential as opposed to commercial but you could simply call it a "property lease agreement" if you want to be succinct, as long as it's clear from the wording of the contract that this is residential property as opposed to commercial property.

What is the difference between a main residence contract and temporary contract?
The difference between a rental contract for a main residence and a fixed-term lease is based on the fact whether the tenant uses the property as a permanent habitual residence or only as a temporary residence. The general legislation for the rental of apartments rather protects the tenants, especially regarding the use of the rental property. However in case of temporary leases for fixed-term periods or seasons (winter, summer, etc..) or periods of less than one year, the tenants rights are less protected, as in this case the parties are authorized to add or to exclude contractually specific paragraphs determined by the locally applicable rental law (Ley de Arrendamientos Urbanos).

What is the difference between a main residence contract and a secondary residence contract?
The difference between the two contracts is in accordance the same as between a contract with main residence and a fixed-term contract. The locally applicable rental law (Ley de Arrendamientos Urbanos) makes a fundamental distinction between: the rental of a property for permanent residential purposes, i.e. the habitual residence and the rental for other, not permanent, purposes.

ya

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Note added at 42 mins (2013-07-10 13:28:13 GMT)
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I think the idea here is that a dwelling is being leased but not as a holiday home or let etc. but as a normal residence.

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Note added at 45 mins (2013-07-10 13:31:08 GMT)
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The general rules for determining "normal residence" are as follows: "normal residence" means the place where a person lives for at least 185 days in each ...

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Note added at 2 hrs (2013-07-10 14:51:01 GMT)
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In Spain it is important to distinguish between leases of property for use as dwelling and other uses as very different laws apply to the two. That's why I would always specify lease of dwelling and then, as here, qualify it.

cf. an assured tenancy agreement vs. an assured shorthold tenancy under the UK Housing Act 1988 that no one has mentioned.

Hence we need to know the EN-lingo target readership: US/Can vs. UK vs. Ireland vs. Oz/NZ etc.

Debatably, the long would reflect the habitual residence component.