I think, hesitantly, that I am a gay man of 60 years of age. I recently came out to my wife after 36 years of marriage. I've been struggling with the question of whether or not I'm truly gay after coming to this conclusion.
I have to figure out how to distinguish between the two. I need to know who I am, and that clarity is crucial. Many therapists have told me that a name is not significant, but for me and how I view myself, it is. I'd be happy to talk about this facet of my sexuality. Are you gay or bisexual take are you gay test.

Gay or Bisexual?
I hear that to you there seems to be a big difference between being gay and being bisexual. You use the phrases “really gay” and “just bisexual”.
Although both identities involve having a physical and/or romantic attraction to a person of the same sex, being gay appears to be more serious in your mind, whereas being bisexual may not be quite as definite.
Perhaps identifying as bisexual would feel less threatening to you? Or maybe you don’t think you deserve the label of “gay”?

You mention your age in your question, which says to me that it is a significant factor in your self-identification. I imagine that changing your sexual identity at this stage in your life comes with a host of heavy feelings.
You may wonder if it is possible to identify as gay after living a heterosexual life for so long. Only you know how long you have felt attraction towards men. Perhaps you have noticed and suppressed feelings for other men for some years.
You do not mention where you are from, but there are very few places where, in the 1950s and 60s, homosexual tendencies were openly accepted and honored. You grew up in generally conservative times when being straight and getting married were societal expectations.
You and your wife may have questions about the validity of your lifelong partnership; have you or she wondered whether you have been “living a lie” all these years? In my opinion, to sustain a partnership with someone for the length of time you have,
It has required great caring, commitment, and compromise throughout the years. Your relationship with your wife is to be honored for exactly what it was and is; it is no less meaningful now that you are ready to explore new romantic territories. And even though you have been in a relationship with a woman for many years, this does not have to be a factor in how you identify your sexuality now, if you don’t want it to be.