Seibu Shinjuku Toll Ltd Exp

While looking at the train routes between Rikugien and my intended eatery near Seibu Shinjuku Station I came across 2 routes - Both starting with Yamanote Line then at Takadanobaba Station I am to change to Seibu Shinjuku Line for Seibu-Shinjuku Station. You see there are 2 almost identical options but price difference is double. One is Shinjuku Line Express [\324) while another one is Seibu Shinjuku Line Toll Limited Express [\724]. Both departing from Platform 5 of Takadanobaba Station. Aside from looking really hard at the approaching trains and verifying it with my google train schedule, how do I ensure I get on the cheaper train? Their trip duration is the same (1 stop). Why the difference in price? Do they look different from each other? Link to the schedules:
https://maps.app.goo.gl/ewpZwovvWvCmRwxY9?g_st=ic

The "Limited express" train have a surcharge upon the base fare, even for one stop. Emphasis on the "Limited" keyword. Express, Rapid trains do not need an additional fee.

1) There is a screen/sign on the side of the train that says "Ltd Exp".
2) It also written on the electric noticeboard above the platform
3) The platform announcements will also say it is a Limited express train.

I don't know what this express train looks like, but I bet it is a bit fancier than the regular one :)

Why dont you continue on Yamanote line to Shinjuku and walk from JR Shinjuku station to your restaurant? Seems way easier and cheaper.

Ya, I’ve decided to just use the Yamanote Line. Nevertheless, thanks for highlighting re Limited part of Express. Useful for other times 🙏