Two routes, two circuits
According to the official Machu Picchu website, Route 1-A (Machu Picchu Mountain) is part of Circuit 1, Panoramic, and Route 3-A (Huayna Picchu Mountain) is part of Circuit 3, Machu Picchu Royalty. The site does not mark either one as high season only, unlike other routes in those circuits.
How to choose between them
To decide, open the official PDF for each route on the circuits page, look at the route and the time slots published by the Ministry of Culture, and pick the one that suits your fitness and your date. The site does not detail quotas or requirements on that page, so confirm any limit directly on the route you choose.
The ticket is separate from the citadel
You choose the route when you get the ticket, not when you arrive. A tour with citadel tickets does not always include the climb: according to the tour listing, the tour with the mountain does include admission to Machu Picchu Mountain, while the one-day tour with tickets includes only admission to the archaeological site. If your plan is Wayna Picchu, ask the operator whether they can arrange it, or buy the ticket yourself.
Which tours appear here
The two cards below show the tour that includes Machu Picchu Mountain and the classic one-day tour without the mountain. According to the listing, the mountain tour sets a minimum age of 18 and is guided in English and Spanish. Check the remaining conditions on the listing before you book.