Marriage

You may only have one marriage to one person. Marriage is nearly always a political institution - usually houses allying or strengthening bonds between friendly houses and factions etc. The participants are not expected to love each other (though a public persona of polite affection is expected, even if it is fake) or even live together. They are expected to sleep together, but it doesn't have to be a regular occurrence (some marriages, especially distant ones, are consummated once a year on holy days).

Consort

May be of any gender and of any number. A consort is a bond of affection at least (usually love). It is the resort of those whose marriage must be used for political purposes as the Seelie court recognises the primacy of love and that those who cement the political structure of the court should not sacrifice love for the purpose. Since this is a bond of love Seelie respect it intensely, even if it is technically ranked below that of a marriage. A Consort does NOT create any kind of political alliance.

Companion

This is not necessarily sexual (but often is). Usually this is a younger Sidhe Companioned to an older, more experienced Sidhe to act like a Lord/Lady in Waiting. Unlike the previous relationships there is a clear difference in status between the 2 Sidhe and the Companion is expected to be submissive and/or subservient. These arrangements are rarely permanent and serve as a kind of apprenticeship for young aristocrats (in politics, life, and sometimes sex). They are also another way of forging political alliances and contacts between houses and ex-Companions usually maintain affection and friendship and are considered to be political allies.

It is rare, but still possible, to have companions between 2 Sidhe of equal age and status as companions - this is usually a convoluted way to form more marriage ties with different Houses. It is not encouraged or desirable, but if a House is short on unattached heirs and is looking for a way to cement some alliances then a convoluted Companion may be the only way since there are no limits to the number of companions a person may have while you may only have one marriage.

Mistress (when in the original Sidhe, the term is unisex)

There is generally some affection but primarily the Mistress is a sexual partner more than anything else. Most Sidhe do not keep Mistresses since they feel no need to give official status to their casual sexual partners. Sometimes a Sidhe wishes acknowledgement for his Mistresses for various reasons (it can give them some of the rights and protections of his household) and the Seelie's excessive order creates a method for that formal acknowledgement.

Mate

A mate is a partner for one purpose - breeding. A relatively new institution, the concept of designated mate has arisen as the birth rate of Sidhe have declined. You can have consorts and Mistresses and Marriages but there is no guarantee of an heir. The mate relationship is very formal - both parties negotiate before the ceremony as to what potential future children will belong to what House, who will see to their upbringing and education, etc. the whole thing is very clinical and all relationship between the two will be entirely focused on producing kids. Technically you can have as many mates as you want but too many is frowned upon since it can spread one bloodline too far (assuming it works).

Pet/Toy

Non-Sidhe bound to a Sidhe. This relationship is OFFICIALLY AND EXPRESSLY NON-SEXUAL. But 9 times out of 10 it is entirely sexual. Basically a Sidhe extends some recognition to a personal companion who is not Sidhe (giving them some status and access). Everyone knows that the Sidhe is probably having sex with the pet, but everyone pretends they're not.