First, counselor and therapist is essentially the same title. When in doubt, take a look at the letters affixed to the end of their name and google those letters. Common ones you'll see are LPC, NCC, LMSW, LCSW, etc. They should all have at a minimum a Master's degree. Most of the highly sought after ones that I've seen hold doctorates.
All therapists/counselors have the same abilities in terms of making referrals for hormones and helping you through coming out and transitioning. The reason many people recommend seeing one who specifically touts themselves as a gender therapist or a therapist specializing in gender, is because they already have the experience of doing those things. But any therapist or counselor has the ability and authority to write you referrals and help you navigate a transition.
There is no special training that counselors/therapists go through to specialize in gender. Usually they have an interest in the subject, a personal connection to it, or have worked with the LGB community in the past and expanded their services to include transfolks. So it really depends on what you're looking for. I wouldn't turn away from a therapist with no gender related experience if they were willing to help me.
If you found this guy on Psychology Today, I'd strongly recommend doing a search here for his name and on other trans sites to see if anyone actually has experience with him. When therapists sign up on that site, they can check as many boxes as they want - there is no one fact checking behind them. Most of them want the most market reach possible, so they check lots of boxes.
