They are phonetically distinct, but not phonemically distinct, which is to say that in most places they occur, they aren't used to distinguish words or meanings.

In particular, the velar nasal "ङ" or "ng" always appears adjacent to a velar sounds (k/kh/g/gh) and similarly the palatal nasal "ञ" always appears adjacent to palatal sounds (c/ch/j/jh), both as allophones of the nasal phonemes "m" (bilabial) and "n" (alveo-dental), basically just like we speak in English under the exact same conditions (like the nasal in the word "English"!)

You perceive a difference with Indic language and English because the Latin script doesn't distinguish nasals for velar and palatal points of articulation - it only distinguishes by bilabial (m) and alveolar (n), whereas Indic scripts do distinguish those, even though they offer no additional information.

The unique nasal sound which is often contrastive in many Indian languages is the retroflex nasal "ण" (ṇ). That's the one that it's easy to confuse in speech if you are not a native speaker, so it's the only one you need to pay extra attention to when learning.

But, as far as I know, the different nasals are phonemic in some languages of India. Which ones depends on which languages, but I do remember seeing at least one in which all four of these were distinct.

None of the major Indian languages I'm familiar with have 4 nasal phones, from either the Indo-Aryan or Dravidian language families.

In the Indo-Aryan languages, the convergence of the various nasals is so complete that they are all often represented with a single "dot" diacritic character when they occur at word junctions.

I'd be open to hearing examples of Indian languages that have 4 nasal phonemes, though.

m (ಮ) n (ನ) ɳ (ಣ) ɲ (ಞ) ŋ (ಙ)

There are 5 nasal glyphs, but like in other Indian languages, 2 (velar and palatal) are allophones of the others, leaving only 3 actual phonemes. Indian scripts are often overspecified, and not every glyph represents a phoneme.