I would date both genders, but I only want sexual relations with one gender. Can someone please tell me what that is called?

To me that sounds like you're sexually&romantically attracted to one gender, but only romantically attracted to the other gender. This is totally possible. Sexual orientation and romantic orientation don't always go hand-in-hand as they are separate things. For example, a person may be heterosexual and biromantic. Or homosexual and biromantic. There are many possible orientations. Some people are bisexual and aromantic (=no romantic feelings), some asexual (=no sexual feelings) and biromantic.

You could be biromantic, but heterosexual/homosexual depending on your gender.

You're most likely biromantic (and then depending on the gender, heterosexual or homosexual). Being biromantic means you're attracted to 2 genders, but aren't necessarily sexually attracted to them. That would be if you were bisexual and biromantic. It's not uncommon for romantic attractions to not match up with sexual ones. So you're most likely biromantic heterosexual or biromantic homosexual.

It sounds like may potentially be attracted to men and women in a romantic way, but only one gender in a sexual way. Sexual and romantic orientation do not always coincide, any combination of the two is possible. This means you can be biromantic while being homo/heterosexual, that's totally possible and normal!

Sexual orientation and romantic orientation are both different things. You could have romantic feelings for one gender but sexual feelings for another. There is a term called biromantic. It is a very large spectrum.

It could possibly mean that you're sexually fluid, you have a preference for both genders and have no possible issues but at the same time, you may choose between being heterosexual or homosexual while being in a relationship. Stay happy, always. x

This would be dependant on your own gender identity. For example, if you are a female who would date both genders but only sleep with men, you would be biromantic and heterosexual. If you would only sleep with females, you would instead be Biromantic and Homosexual. Your gender helps identify the name of your sexual preference. Your romantic feelings relate to the romantic side of your identity. Several terms such as androsexual and gynosexual refer to being attracted to masculinity or femininity, respectfully. I hope this helps you find an answer to your question, but remember that labels aren’t for everyone, and not everyone sees labels as the same!