There are two types of senses in 5e: vision, and everything else.
Vision covers normal sight, and includes: Blindsight, Darkvision, and Truesight. Other senses include: hearing, and tremorsense
If you can detect something with any sense, then you know its location at the very least. If you can hear something, then you can tell what it sounds like. If you can see something you can tell what it looks like. Fairly straightforward.
There are a few benefits unique to sight. For example the Unseen Attackers and Targets section applies only to vision (or lack thereof):
When you attack a target that you can't see, you have disadvantage on the attack roll. This is true whether you're guessing the target's location or you're targeting a creature you can hear but not see. If the target isn't in the location you targeted, you automatically miss, but the DM typically just says that the attack missed, not whether you guessed the target's location correctly.
When a creature can't see you, you have advantage on attack rolls against it. If you are hidden--both unseen and unheard--when you make an attack, you give away your location when the attack hits or misses.
If you can't see or hear a target, then you will have to guess its location.
An invisible creature cannot be seen
Being invisible means you cannot be seen, but you can be heard:
An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. The creature's location can be detected by any noise it makes or any tracks it leaves.
- An invisible creature cannot be seen
- But it can be heard so its location is known
- It attacks with advantage
- Attacks against it have disadvantage
A hidden creature cannot be seen, and cannot be heard (so long as it doesn't make noise!)
The rules for Hiding state:
When you try to hide, make a Dexterity (Stealth) check. Until you are discovered or you stop hiding, that check's total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence.
You can't hide from a creature that can see you clearly, and you give away your position if you make noise, such as shouting a warning or knocking over a vase.
- A hiding creature cannot be seen
- It cannot be heard (unless it makes noise) so its location is unknown
- It attacks with advantage, and when it does the location it attacks from is revealed
- Attacks against it have disadvantage, and you have to guess the creature's location
Hiding is better than being invisible
A hiding creature's location is unknown. This makes it harder to fight against. If you want to attack the creature, you need to guess its location. If you guess wrong, the attack automatically misses.
If a hiding character's stealth check is beaten by someone, then hiding has no benefits against that person. In your situation, that means that the invisible player's location will be known, their footsteps can be heard or other evidence can be detected.