Binaural beats are created from two different continuous tones, which when sent separately to each ear create a single beat inside your head. Isochronic tones are basically a single tone which is switched on and off at regular intervals. Imagine a single continuous tone playing on a stereo system and you’ve got your hand on the volume switch. Then once per second, you turn the volume off for half a second and keep doing that every second. For half a second the volume is off, for the other half a beat waveform is formed. The beat is cycling once per second per second, i.e. at a rate of 1Hz.
Anxiety: In a review of brainwave entrainment research, there were several studies that investigated short-term stress relief as well as long-term stress or “burnout.” Several used modalities of auditory stimulation, while a couple used audio-visual entrainment. Those with heightened short-term stress and anxiety were undergoing medical treatments, experiencing addiction, and/or were just anxious adults.

Additionally, most of the studies have been conducted with extremely small samples and the touted benefits are vague. When studying the effects, it would be beneficial to hook each participant up to an EEG, note initial brainwave activity, then post-entrainment, note any changes. Although certain conditions share similarities in brainwave activity, this is clearly not always the case.
Isochronic tones work just the same in delta as they do in alpha, theta and beta and they are widely used in the brainwave entrainment community to help people sleep. Like you, I’ve also seen some websites saying they don’t work in delta, but it’s a bit like the game of Chinese Whispers, where someone makes a comment and then after it gets passed around and shared a lot the message gets distorted and appears to be a fact. I don’t know of any scientific reason why they wouldn’t work in delta. I remember some people talking about this on a brainwave entrainment forum many years ago. They were saying they found isochronic tones a bit too abrupt for using to help them sleep and they preferred binaural beats, as they thought they were a more soothing sound. That was just a personal preference shared by a couple of prominent forum members at the time and some people then took that as a fact for everyone. That’s where I think that belief originated from.
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Subsequently, the term 'entrainment' has been used to describe a shared tendency of many physical and biological systems to synchronize their periodicity and rhythm through interaction. This tendency has been identified as specifically pertinent to the study of sound and music generally, and acoustic rhythms specifically. The most ubiquitous and familiar examples of neuromotor entrainment to acoustic stimuli is observable in spontaneous foot or finger tapping to the rhythmic beat of a song.

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