Separate property is typically property that you owned before you got married. It also includes property that you inherited, even if you inherited it after you got married. Property that was acquired after the marriage but may be titled in only one of the parties' names is considered community property, not separate property.
Joint property (community property) is property that you acquired with your spouse during the marriage, no matter if it is only in the name of one of the parties. Keep in mind, however, that a community property interest in separate property can be later acquired by a spouse in some situations. For example, if one party had a rental property before they were married, but joint/community funds were used to take care of that property (mortgage payments, taxes, maintenance, etc), an unrecorded community property interest for the spouse that is not on title may accumulate a community property interest in that property.