Tandra refers to a state of being while Tantra is a method for attaining liberation.
Lineage differ significantly in where they place the meditative state of tandra on the spectrum of experience. A few seem to place it as a more advanced state, but the general agreement is that tandra is one of the first meditative states likely to be experienced by a yogi.
The word, tandra, means "drowsiness" or "lethargy" in many contexts. With respect to meditation, tandra is a meditative state in which the action of the mind is pacified and the meditator feels peaceful. The mind is not clear or luminous, however, and the meditator does not experience the expansive non-dual awareness that characterizes deeper states of meditation.
This early meditation stage is called tandra because of the drowsy, peaceful, disconnected feeling it produces. Tandra is not samadhi. For details on tandra as part of your lineage, I suggest also asking a lineage-holder teacher.
(For the answer to a related question: Why do I get sleepy when I meditate?)
Tantra is a method for reaching moksha (liberation or enlightenment) characterized by the use of mundane experience as an instrument for experiencing divine bliss. The basic philosophy of tantra is the spirit and matter are of the same essence; there is nothing to be transcended, except our own ignorance.
Tantric practices developed as a reaction against empty ritualization in orthodox Vedic and Buddhist practice; according to Tantra, divine awareness is ever-present. While there are advanced Tantric practices considered transgressive by non-Tantrics, their purpose is to transcend mental constructs. The Sanskrit root, tan, indicates expansion, and the purpose of Tantric practices is to break free from conceptual confinement.
The word, Tantra, can mean "web" or ‘"thread," and these physical referents are metaphors for Tantric yoga practices in the sense that they reflect the fundamental unity of all things. Rather than dividing experience into divine and mundane, physical and spiritual, sacred and unclean, the Tantric path considers all of existence to be a manifestation of the Divine.
Finally, it is worth noting that while tandra can be part of a Tantric practice, such meditative states exist in orthodox practice, too. While the words look similar, they are not subsets of or prerequisites to one another.
(Continue reading for the answer to a related question: What is the secret of meditation?)