Someone may use transsexual to describe themself while another person prefers transgender or trans. The Trans Journalists Association notes that transsexual has a narrower contemporary usage, that some people find it outdated or offensive, and that self-description matters. In a dating conversation, you do not need to decide which label another person should adopt.
Follow the wording someone gives you
Imagine you have been talking with a person who uses transsexual in their introduction. You can use their name and discuss the interests they mentioned without opening a debate about that word. If they explicitly ask you to use a particular description, keep that request in mind. It is their description of themself, not permission to apply it to everyone you meet.
The reverse situation deserves the same care. If someone says they do not want that word used for them, remove it from your messages about them. Explaining where you originally learned it does not need to become a long argument. A brief acknowledgment and changed wording are more useful than repeatedly asking them to reassure you.
Separate a label from a personal question
A term in a profile is not an invitation to request photographs, details of treatment, or an account of earlier relationships. Before asking a sensitive question, identify the actual decision you are trying to make together. “What would make this first meeting comfortable?” gives the person room to choose what is relevant. A demand for their complete history does not.
You can also state your own practical needs without demanding a disclosure. For example, you may prefer a short first meeting because you have limited time. Explain the time limit directly rather than linking it to uncertainty about someone's identity.
Check introductions before involving other people
Before introducing a date to friends, agree on what you will say. “This is Alex; we met through a dating app” may be all that is needed. Ask before sharing an identity label from a private conversation, even if it appeared somewhere online. If your date wants to make their own introduction, leave room for that choice.
Terminology source
Trans Journalists Association: Stylebook and Coverage Guide. Its terminology entry informs the opening paragraph. The conversation examples are editorial suggestions, not clinical guidance or a requirement to disclose personal information.